The Algebra of Metaphysics © Les Éditions Chromatika, 2010; www.chromatika.org Dépôt légal: D/2010/11.353/4 ISBN 978-2-930517-08-7 Printed in Belgium No part of this book may be used or reproduced in any manner whatsoever without the prior permission in writing of the publisher (editions@chromatika.org). Diffusion: www.i6doc.com & www.vrin.fr On order in bookshops or via Diffusion universitaire CIACO, 1348 Louvain-la-Neuve, Belgium, duc@ciaco.com  Edited by Ronny Desmet and Michel Weber Whitehead The Algebra of Metaphysics Applied Process Metaphysics Summer Institute Memorandum  Contents Abbreviations ...................................................................................7
Preface — Michel Weber ..................................................................9
I. Introduction Michel Weber ............................................................................13
II. Reading Whitehead Randall E. Auxier ......................................................................59
III. Whitehead’s Cambridge Training Ronny Desmet ..........................................................................91
IV. A Refutation of Russell’s Stereotype Ronny Desmet ........................................................................127
V. Was Whitehead an Analytical Philosopher? Ronny Desmet ........................................................................211
VI. Whitehead on Mathematics Education in the 1910s Ivor Grattan-Guinness..............................................................249
VII. Subject and Object in Whitehead’s Metaphysics John B. Cobb, Jr.......................................................................269
VIII. The Rationality of Consciousness Michel Weber ..........................................................................277
IX. Vision of Existence and Politics of Being Michel Weber ..........................................................................343
X. Whitehead’s Relativity Ronny Desmet ........................................................................365 List of Contributors.......................................................................375
 Abbreviations ADG The Axioms of Descriptive Geometry, Cambridge, 1907. APG The Axioms of Projective Geometry, Cambridge, 1906. AE The Aims of Education, 1929 (Free Press, 1967). AI Adventures of Ideas, 1933 (Free Press, 1967). CN The Concept of Nature, 1920 (Cambridge, 1964). D Lucien Price, Dialogues, 1954 (Mentor Book, 1956). ESP Essays in Science and Philosophy, Philosophical Lib., 1947. FR The Function of Reason, 1929 (Beacon Press, 1958). IM An Introduction to Mathematics, 1911 (Oxford, 1958). IS The Interpretation of Science, Bobbs-Merrill Co., 1961. MCMW “On Mathematical Concepts of the Material World,” 1906. MT Modes of Thought, 1938 (Free Press, 1968). OCN “On Cardinal Numbers,” 1902. OT The Organisation of Thought, Williams and Norgate, 1917. PM Principia Mathematica, 1910–1913 (Cambridge, 1925–1927). PNK Principles of Natural Knowledge, 1919/1925 (Dover, 1982). PR Process and Reality, 1929 (Corrected edition, 1978). R The Principle of Relativity, Cambridge, 1922. RM Religion in the Making, Macmillan, 1926. S Symbolism, Its Meaning and Effect, Macmillan, 1927. SMW Science and the Modern World, 1925 (Free Press, 1967). TRE “La théorie relationniste de l’espace,” 1914. UA A Treatise on Universal Algebra, Cambridge, 1898.  Preface Michel Weber Alfred North Whitehead (1861–1947) claimed that “to sustain a civiliza- tion with the intensity of its first ardour requires more than learning. Adventure is essential, namely, the search for new perfections” (AI 258). Hence, albeit at a different scale, the Applied Process Meta- physics Summer Institute created in 2010 at the Cité universitaire’s Fondation Biermans Lapôtre (Paris), attempts to secure the proper at- mosphere to envisage Whitehead’s vision and peruse its intricate expositions in a way that encourages both individuation and solidarity while preventing dogmatism. Applied process metaphysics seeks in- deed to provide —and to move beyond— detailed technical renderings of process philosophy.1 What matters is each person’s variegated ex- perience, how to refresh our shared understanding of it, and, thereby, how to foster civilization. The readings for the course will be a collection of memoranda in two senses: an introductory booklet that helps unpacking the arguments, and a record of the proceedings. For the participants of the Summer Institute, it will support the lectures and spur the discussions; for the scholars not in attendence looking for a focused introduction to White- head’s legacy, it will provide benchmark arguments. The Summer Institute is an international forum dedicated to the cross- examination of Whitehead’s “organic” or “process” thought and the various facets of the contemporary philosophical field of research and debate. Bold speculations balanced by “complete humility before logic, and before fact” (PR 17) are especially valued. “It is a disease of phi- 1 Cf. Mark Dibben and Thomas Kelly (eds.), Applied Process Thought I: Initial Explorations in Theory and Research, Frankfurt / Lancaster, ontos verlag, 2008, p. 27. 10 Michel Weber losophy,” stresses Whitehead, “when it is neither bold nor humble, but merely a reflection of the temperamental presuppositions of excep- tional personalities” (PR 17). Drawing upon the major Harvard works —Science and the Modern World (1925), Process and Reality (1929) and Adventures of Ideas (1933)—, the essays gathered here seek, first, to introduce into White- head’s thought by clarifying what is at stake in his philosophy and by providing a synoptic vision of his key categories in light of their histori- cal development, and, second, to foster a creative dialogue among all participants. They give us the opportunity to travel through most as- pects of Whitehead’s legacy: anthropology, ecology, education, epistemology, metaphysics, psychology, political theory, quantum me- chanics and relativity physics. All share the common characteristic of being written by acknowledged Whiteheadian scholars who have kept a youthful praxis. Youth is not defined by years but by the creative impulse to make something. The aged are those who, before all things, desire not to make a mistake. Logic is the olive branch from the old to the young, the wand which in the hands of youth has the magic property of creating science. (AE 119) What authors provide here is akin to a cavalry charge in a battle1—the battle to grasp Whitehead secundum Whitehead and to put him to the test of contemporary challenges. The bulk of the material that is published here for the first time comes from R. Desmet’s outstanding Ph.D. thesis (Vrije Universiteit Brussel, 2010). 1 “It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise op- posite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle— they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.” (IM 41-42)  Preface 11 “Denken ist Danken.” All the scholars involved in this new venture have to be thanked for their important input and for their collaboration: Randall E. Auxier (Southern Illinois University Carbondale, U.S.A.), Vin- cent Berne (Université de Paris I-Panthéon Sorbonne, France), John B. Cobb, Jr. (Claremont School of Theology and Claremont Graduate Uni- versity, U.S.A.) Godehard Brüntrup (Hochschule für Philosophie, München, Germany), Michael Chartier (University of Saskatchewan, Saskatoon, Canada), Émeline Deroo (Université de Liège, Belgium), Ronny Desmet (Vrije Universiteit Brussel, Belgium), Jonathan Durand Folco (Université Laval, Québec, Canada), Ivor Grattan-Guinness (Mid- dlesex University, Great-Britain) Ludwig Jaskolla (Hochschule für Philosophie, München, Germany), Eleonora Mingarelli (Università di Milano Statale, Italy), Sanne Stuur (Radboud Universiteit Nijmegen, Netherlands), Olivier Thiery (Université de Paris X-Nanterre, France). Last but not least, to the director and the deputy director of the Bier- mans Foundation, Jozef Aelvoet and Claude Gonfroid, I owe a very special thanks for their unflinching support in this project.  I Introduction Michel Weber The Whiteheadian legacy is exceptionally rich, both because of the various expertises and the character of A.N. Whitehead himself, who worked in most scientific areas of his time, and also because of the contemporary challenges in philosophy, techno-science and politics. According to Hilary Putnam, scientists acknowledge nowadays the con- tribution of only three “philosophers”: I. Kant (in astronomy with his 1755 Nebular Hypothesis), C.S. Peirce (in geodesy, gravimetry and Pho- tometry in 1878) and Whitehead (in relativity with his 1922 Principle). Of course this list would be very long if one were to take account of all actual philosopher-scientists: we would have to go as far back in the Western tradition as the Presocratics, and give much attention to Des- cartes, whose influence (especially in the cognitive sciences) has been lasting and remarkable and who could be seen as Whitehead’s arch- enemy—even though he fostered the modern “subjectivist bias” and anticipated the merging of space and matter.1 However, given the state- of-the-art in the sciences and the humanities, Whiteheadian process thought remains the most promising, both from a synthetic perspective (because of its capacity to bring together, i.e., coherently articulate, all gnoseological fields both within and without philosophy) and from an analytic one (because of its potentiality for contributing to—if not solving—topical conundrums). Last but not least, Whiteheadian pro- cessism is intrinsically critical, both in the transcendental and pragmatic senses (it is fully aware of the limitations of intuition, sense- perception, language and rationality) and in the fallibilist one (applic- ability matters as much as coherence while adequacy remains out of 1 Cf., e.g., R 38 and PR 73 sq. 14 Michel Weber reach): hence, new light is cast on the crucial arguments of Kant, Peirce and Popper. This introduction will sketch Whitehead’s life and works, present his legacy, and offer some remarks about the Urizen of process thought.1 1. Brief Vita Born on 15 February 1861 at Ramsgate (Kent, United Kingdom) and deceased 30 December 1947 at Cambridge (Massachusetts, United States), Whitehead attended the Sherborne public school (Dorsetshire) where “classical studies were interspersed with mathematics” (ESP 6) before entering Trinity College in 1880 with a scholarship in mathemat- ics. In 1884, he was elected Fellow in Mathematics with a dissertation (now lost) on Maxwell’s Treatise on Electricity and Magnetism (1873) and started teaching mathematics and mathematical physics. In 1905, he received a Doctor of Science degree on the basis of his Universal Algebra (1898) and of his four American Journal of Mathematics papers (1901–1904). In 1910 he resigned his Lectureship and moved unex- pectedly to London, where he was an independent scholar for a year, then taught at University College London for three years and moved finally to the Imperial College of Science and Technology (London), where he taught the same subjects until 1924. According to the chron- ology Victor Lowe masterfully established, President A. Lawrence Lowell wrote formally to Whitehead on February 6, 1924 to invite him to teach philosophy at Harvard University.2 Although the matter was in 1 This chapter is inspired by two previous publications of mine that are here updated: “Introduction” in Michel Weber and William Des- mond, Jr. (eds.), Handbook of Whiteheadian Process Thought, Frankfurt / Lancaster, ontos verlag, 2008, I, pp. 15-38; and “The Urizen of Whiteheadian Process Thought” in Mark Dibben and Rebecca Newton (eds.), Applied Process Thought II: Following a Trail Ablaze, Frankfurt / Lancaster, ontos verlag, 2009, pp. 61-73. 2 Victor Augustus Lowe, A. N. Whitehead. The Man and His Work. Vol- ume I: 1861–1910; Volume II: 1910–1947 (edited by J. B. Schneewind), Baltimore, Maryland and London, The Johns Hopkins  Introduction 15 the air—at least within Harvard’s “Royce Club”—since 1920 and an informal inquiry took place in January 1924, it seems that the formal invitation was a “complete surprise” for Whitehead and that he was immediately very enthusiastic: “I would rather do that than anything in the world,” he said to his wife.1 The Whiteheads left on August 15 and reached Boston on August 27. He started to lecture on September 23 at the Department of Philosophy, which was probably expecting only classes and new publications in logic and the philosophy of natural sciences. Whitehead, however, immediately embraced a far more speculative standpoint that became straightforwardly metaphysical one year later when he published the course of lectures he had given at the Lowell Institute (upon the invitation of A.L. Lowell, who was then the sole trustee of the Institute). Emeritus in 1937, Whitehead continued to work at a slower pace until his death. Upon his request, all his unpub- lished papers, letters and notes were burned either by Weiss or by Hartshorne.2 He was cremated and his ashes scattered in the graveyard of Harvard's Memorial Church where a service was held for him on 6 January 1948. Whitehead’s lasting philosophical outlook is characterized by a con- stant desire to question the meanings of “simple obvious statements” (R 40) and to reorganise general ideas in order to attain higher orders of abstractions—while being critically aware of the limitations of lan- University Press, 1985 & 1990. See also William Ernest Hocking’s testimony in “Whitehead as I Knew Him,” Journal of Philosophy, 58, 1961, pp. 505-516, reprinted in George Louis Kline (Edited and with an Introduction by), A. N. Whitehead: Essays on His Philosophy, En- glewood-Cliffs, New Jersey, Prentice-Hall, Inc., 1963, pp. 7-17 (Corrected reprint: University Press of America, 1989). 1 According to Lucien Price's Dialogues of A. N. Whitehead. Introduction by Sir David Ross, Boston/London, Little, Brown & Company, 1954. We quote the reprint in Mentor Book, 1956, p. 14. 2 Very few letters and papers escaped, mainly thanks to V. Lowe, B. Russell and R. B. Haldane: they can be consulted in the Milton S. Eisenhower Library (Johns Hopkins University), in the Mills Me- morial Library (McMaster University), and in the Haldane Archives (National Library of Scotland). 16 Michel Weber guage. This twofold tension nourishing his speculations can be specified as follows: towards a radical empiricism on one hand, and a complete formalism on the other.1 One can see, in other words, that the so-called Analytic-Continental divide has always already been obsolete for White- head. His turn towards a radical empiricism is informed essentially by a plu- ralism and an attention to the interconnectedness of events. Of course, it is somewhat daring to speak of a Whiteheadian radical empiricism before 1924, but this becomes nevertheless possible because of the importance of relations in all his writings. The other trend in Whitehead, towards a complete formalism, took on various guises during his career. His formalizations remained indeed open to the conceptual revolutions of his time: the early Whitehead is particularly sensitive to the recent foundational developments in alge- bra and geometry; his middle period particularly tackles electromagnetism (including the nascent quantum mechanics, as in Planck, Einstein, and Bohr) and Einstein’s theories of relativity (includ- ing Poincaré and Minkowski); the late Whitehead also shows the influence of contemporary thinkers like S. Alexander, H. Bergson, F. H. Bradley, C. D. Broad, J. Dewey, L. J. Henderson, W. James, J. McTag- gart, G. H. Mead, G. Santayana, and, of course, B. Russell.2 In the background, the systems of Plato, Aristotle, Descartes, Galileo, Hume, Kant, Leibniz, Locke and Newton stand out as well. Needless to say, both lists are not exhaustive, especially because Whitehead was an 1 This is also testified by Andrew Dawson and scholars such as Emmet (see her “A. N. Whitehead: The Last Phase,” Mind, 57, 1948, pp. 265-274), Hocking (see his “Whitehead as I Knew Him,” op. cit.), Al- lison Heartz Johnson (“Whitehead as Teacher and Philosopher,” Philosophy and Phenomenological Research, Vol. 29, 1968-1969, pp. 351-376), and Joseph Gerard Brennan (“Alfred North Whitehead: Plato's Lost Dialogue”, The American Scholar, 47, 4, 1978, pp. 515- 524). 2 Here the interplay between the speculations and personal lives of Russell and Whitehead is a subject unto itself, and one made all the more difficult because Whitehead left very few clues while Russell’s numerous testimonies are often unreliable.  Introduction 17 introvert by temperament and does not always reveal his influences, because his library was dispersed on the occasion of his several moves, because of the change of orientation of his research program and, final- ly, because of the clauses of his will. Unfortunately, a treasure chest such as the one his good friend Keynes discovered in 1936 with all Newton’s unpublished manuscripts does not seem to be available. 1 The development of his thought can be divided into three periods which exemplify his lasting outlook in different ways, placing emphasis respectively on logic, epistemology, and metaphysics. An examination of these three “canonical” epochs reveals that Whitehead respectively contemplates (i) the logico-mathematical field sub specie totalitatis, where he aims at the ultimate generalities (for which reason the logicist program was once appealing to him) and at disclosing reality’s funda- mental pattern (for which reason we can speak of his formal ontology2); (ii) geometry as a physical science, both in the sense that geometry frames common sensical perception and science and that it can be extracted from them; and (iii) metaphysics under the category of cre- ativity for, prima facie, Process and Reality indeed offers a genetic calculus of creative intension (for which reason one can speak of an existential ontology3) but it works hand-in-hand with a morphological calculus of created extension. There is thus a common double thread or root-metaphor to these three dimensions—the assessment of the ques- 1 John Maynard Keynes, “Newton, the man,” in The Royal Society New- ton Tercentenary Celebrations, 15-19 July 1946, Cambridge University Press, 1947, pp. 27-34. Cf. Loup Verlet, La malle de New- ton, Paris, Gallimard, 1993. 2 The well-known contrast between formal logic and formal ontology is Husserlian (see his Logische Untersuchungen III, 1900–1901, that, incidentally, also sketches a theory of part and whole), but it can be traced back to Aristotle and Grassmann, the later being extremely important to Whitehead. 3 The contrast between formal and existential ontology is exploited in M. Weber’s “PNK's Creative Advance from Formal to Existential On- tology,” in Guillaume Durand et Michel Weber (sous la direction de), Les principes de la connaissance naturelle d’Alfred North White- head—Alfred North Whitehead’s Principles of Natural Knowledge, Frankfurt, Ontos Verlag, 2007, pp. 259-273. 18 Michel Weber tions of uniform (spatial) extension and of relationality—that boils down to one single character, broadly understood: relativism. For- malism is always only a tool (an organon) to come to terms with reality understood from the standpoint of a relationist theory of extension. More precisely, one finds the same Fregean pattern throughout Whi- tehead’s development: a primitive polyadic relation operating upon a field or domain of relata.1 The relation is sometimes generalized, as in the case of MCMW’s pentadic relations, but usually Whitehead uses a basic dyadic relation (of the type aKb) activated in a web of relationship (it is the case that aKb, but also that aKc, aKd…). The three emblematic works are UA, PNK and PR (MCMW’s 1905 “Theory of Interpoints” providing the continuity seemingly interrupted by PM). In UA, rules of equivalence and of derivation (such as addition or mul- tiplication) operate on a Grassmannian-Riemannian manifold of abstract elements. If the elements are vectors, the abstract algebraic approach can be applied to Maxwell's theory of electricity and magnet- ism. The immediate goal is to elucidate the ontological weight of Maxwell’s equations. Uniformity is treated with the concept of equiva- lence grounded in linear strains. In PNK, the (mereological) relation of extension operates on the con- tinuous field of events. The goal is to understand the foundations of sense-perception, as it is exploited by common-sense and by the sci- 1 The predicate Fregean is used loosely, especially since it is not clear to what extent Whitehead knew Gottlob Frege’s works (esp. Die Grund- lagen der Arithmetik. Eine logische-mathematische Untersuchung über den Begriff der Zahl, Breslau, Verlag von Wilhelm Koebner, 1884; “Funktion und Begriff,” Vortrag, gehalten in der Sitzung vom 9. Januar 1891 der Jenaischen Gesellschaft für Medecin und Naturwis- senschaft, Jena, 1891; “Über Sinn und Bedeutung,” Zeitschrift für Philosophie und philosophische Kritik, Vol. 100, 1892, pp. 25-50) be- fore the publication of Russell’s Principles of Mathematics in 1903. James Bradley makes a similar claim that Whitehead generalizes the Fregean approach of applying propositional functions in his “The Generalization of the Mathematical Function: A Speculative Analy- sis,” in Guy Debrock (ed.), Process Pragmatism. Essays on a Quiet Philosophical Revolution, Amsterdam, Rodopi, 2004, pp. 71-86.  Introduction 19 ences: hence the “method of extensive abstraction” using the notions of “convergence” and “equivalence class” (directly imported from the Principia Mathematica, perhaps under the influence of Frege’s works). Uniformity is treated with the concept of congruence that provides the framework for understanding coincidence, recognition and measure- ment.1 PR introduces the relation of extensive connection operating on re- gions. Its purpose is to display the gearing of actuality per se or existence (which is subjective and qualitative) and of the various layers of potentiality or being (basically objective and quantitative). PR thus transcends Whitehead’s previous formal ontological standpoint with a proper existential ontological standpoint. Uniformity is again treated with congruence, which is conditioned by ovateness.2 Furthermore, whereas previous systematic attempts bore the obvious seal of other mathematicians and physicists, Whitehead is here tapping his own resources (besides the reference he makes to Th. de Laguna) and draw- ing the metaphysical consequences of his adoption of an epochal theory of time. Yet another way of sketching the developmental trajectory would be as follows: in Cambridge, Whitehead focused on the a priori knowledge that can be extracted from the knower; in London, on the a posteriori knowledge imposed by the known; while in Harvard, he attempted a synthesis of the knower and the known.3 Let us now peruse the main publications of the philosopher. 1 As PR 328 claims: “although ‘coincidence’ is used as a test of congru- ence, it is not the meaning of congruence.” 2 “The systematic character of a continuum depends on its possession of one or more ovate classes” (PR 307). For its part, the actual meaning of congruence requires the introduction of strain feeling (PR 330). 3 Cf. PNK vii: “We are concerned only with Nature, that is, with the object of perceptual knowledge, and not with the synthesis of the knower and the known.” 20 Michel Weber 1.1. Cambridge, U.K. (1880–1909) A Treatise on Universal Algebra (1898) was Whitehead’s first book. It is largely based on a thorough investigation of Grassmann’s calculus of extension (Ausdehnungslehre, 1844), Hamilton’s Quaternions (1853), Boole’s algebra of logic (Symbolic Logic, 1859), Benjamin Peirce’s Lin- ear Associative Algebra (1870) and Riemann’s Manifold (“Über die Hypothesen, welche der Geometrie zu Grunde liegen,” 1867). Further- more, as its title displays, Leibniz’s shadow (under the guise of the “Ars combinatoria”) leads him to the quest of a “universal calculus to facili- tate reasoning in connection with every province of thought, or of external experience.” (One should note that Russell’s and Couturat’s Leibnizian inquiries are yet to appear.) His thesis is that mathematics (in its widest signification) is not simply the science of number and quantity, but a highly efficient universal engine of investigation of the possibilities of thought and reasoning: Whitehead's algebra avoids the restriction of variables to symbols for particular numbers (cf. his inter- est in projective geometry) to elaborate a fully-fledged logic of propositions (“the sole concern of mathematics is the inference of proposition from proposition”). The planned second volume never ap- peared, being factually replaced by the co-authorship of the Principia Mathematica. “On Mathematical Concepts of the Material World” (1905) is an ambi- tious comparative study of five logical constructs describing the possible ways of conceiving a priori the structure of the physical world. It is written with the reformed symbolism of the forthcoming Principia (itself based on Peano’s conventions). Whitehead looks for nothing less than the “fundamental relations” acting between “ultimate existents.” The monograph launches the trenchant criticism of Newtonian materi- alism that will mainly occupy his next periods, and introduces various other forthcoming features as well, such as the “theory of interpoints,” which clearly anticipates his “method of extensive abstraction.” The background to this work is James Clerk Maxwell's thought and the natural philosophy (in the loose sense of the word) of John Henry Poynting, Joseph John Thomson and Joseph Larmor, as well as the  Introduction 21 work of George Gabriel Stokes, William Thomson (later known as Lord Kelvin) and Peter Guthrie Tait. Russell came up to Trinity in 1890 and followed Whitehead's and J. Ward’s lectures. In 1897 appeared his Foundations of Geometry; in 1903, he published The Principles of Mathematics and soon discovered the possibility of a synergy between his planned second volume and the second volume of the Universal Algebra that was still in the air. As a result, the authors decided to unite their efforts. Principia Math- ematica’s bold program of deducing mathematics from a set of logical axioms stems from the above mentioned works plus Peano’s theory of natural numbers (Arithmetices principia nova methodo exposita, 1889; Formulario di mathematico, 1895), Cantor’s transfinite arithmetics (Grundlagen einer allgemeinen Mannichfaltigkeitslehre, 1883) and Frege’s foundational inquiries (Grundlagen der Arithmetik, 1884). Ac- cording to Russell, Whitehead especially contributed the treatment of “apparent variables” (PM IB), “identity” (IB), “cardinal arithmetic” (Parts II & III), “convergence and limit of functions” (VC), and “quan- tity” (VIB & C). He concludes: “In most parts of the book, there was, in the end, very little for which either had sole responsibility.”1 On the whole, Whitehead was especially active in Parts II (where he was re- sponsible for the blunder on the nature and number of individuals), V, and VI. Thanks to Gödel’s Incompleteness Theorem, it is now accepted that logicism—the understanding of arithmetic (and much more of math- ematics) as an extension of deductive logic—is mistaken. However, Principia Mathematica remains an intellectual landmark of the twenti- eth century, not only for its famous Theory of Types, but also as the final (though not the first) break with the Aristotelian subject-predicate logic. 1 “Whitehead and Principia Mathematica,” Mind, Vol. LVII, N° 226, 1948, pp. 137-138; for a non-technical introduction to the Principia, see Whitehead’s Aims of Education or Russell’s Introduction to Mathematical Philosophy, 1919. 22 Michel Weber An Introduction to Mathematics (1911) is a popularizing work laying stress on the empirical basis of mathematics. It constitutes a straight- forward introduction to the methods and applications of mathematics (broadly understood). Written for the layman, it is nevertheless quite illuminating regarding Whitehead's lasting philosophical outlook. The fourth volume of the Principia was supposed to be written by Whitehead alone. In order to be able to properly discuss the geometry of the world, around 1905 he launched a series of new inquiries, that would culminate in a personal reassessment of Einsteinian relativity (i.e., the replacement of the variable curvature of space-time by multi- ple time-systems constituting a flat or pseudo-Euclidean space-time). In other words, the completion of the Principia is simply postponed and he begins his journey in epistemology. The genesis of non-Euclidean geometries (Gauss, Lobachewsky, Bolyai, Riemann, Helmholtz) had occupied Whitehead during his entire life; now he went on to exploit philosophically the concepts of “field” and “vector” as well. 1.2. London (1911–1924) The London years saw the publication of three books of similar inspira- tion: An Enquiry Concerning the Principles of Natural Knowledge (1919, 2nd. ed., 1925), The Concept of Nature (1920), and The Principle of Relativity. With application to Physical Science (1922). Their goal is to be useful for mathematicians, scientists and philosophers. Throughout their respective developments, the basic questions remain: what is “Nature” (i.e., the object of perceptual knowledge); how are time and space rooted in direct experience; and what shape could (should) the simplest generalization from immediate evidence take? The answer takes the form of a careful study of the presuppositions of modern sci- ence, with special attention given to Newton, Maxwell, Larmor, Lorentz, Minkowski and Einstein. Whitehead insists on the necessity of satisfying both science and common sense. Hence the two main fea- tures of his epistemology: the systematization of the concepts of event and object, and their instrumentalization by the “Method of Extensive Abstraction,” which constitutes a skilled generalization of the instinctive procedure of habitual experience with the help of the logic of relations.  Introduction 23 Both features result from his denunciation of the “bifurcation of na- ture,” i.e., of the Galilean dichotomization between nature as sensed and nature as postulated by science and of the subsidiary Lockean bi- furcation between primary and secondary qualities. The substance- oriented physics, dualistic in essence, is utterly replaced by a physics of events, at three complementary levels: extension no longer expresses disconnection between substances but connectedness between events; instants are replaced by durations; and absolute space is replaced by a relational/connectionist account of spatio-temporality. In the Preface to the second edition of the Principles of Natural Know- ledge (dated August, 1924—remember the Whiteheads left London for Liverpool on August 15 and reached Boston on August 27)—Whitehead was already stating that he hoped “in the immediate future” to embody the standpoint of his epistemological inquiries “in a more complete metaphysical study.” And he did so in a rather revolutionary way. What begins to matter indeed is the intelligence of the ontological conditions of possibility of the “creative advance of nature.” The full systematic— or rather, heuristic—answer will be given by Process and Reality; but three other works particularly matter: the pre-systematic Science and the Modern World and Religion in the Making, and the post-systematic Adventures of Ideas.1 1.3. Harvard (1924–1947) Science and the Modern World (being the Lowell Lectures of 1925) em- bodies perhaps the first critical historico-conceptual study of the development of modern science ever, starting with the Greeks, survey- ing 2500 years of techno-scientific struggles with “stubborn facts,” and devoting special attention to the Einsteinian upheaval and the nascent quantum mechanics. These lectures ran from February to March 1925 1 Needless to say that our use of “pre-systematic” and “post-systematic” differs from Christian’s (cf. “Some Uses of Reason”, in Ivor Leclerc (ed.), The Relevance of Whitehead. Philosophical Essays in Com- memoration of the Century of the Birth of Alfred North Whitehead, London/New York, George Allen and Unwin Ltd./Humanities Press Inc., 1961, pp. 47-89). 24 Michel Weber and were published—”with some slight expansion” according to SMW’s Preface—in October 1925. The added material consists of two gener- alist chapters that were delivered as lectures in other circumstances (Chapter II on Mathematics as an Element in the History of Thought and Chapter XII on Religion and Science) and two brand new chapters (Chapter X on Abstraction and Chapter XI on God), both especially re- flective of an ontological orientation. Science and the Modern World constitutes Whitehead's earliest careful exploration of the everlasting ontological problem—how to understand the “coming-to-be and passing-away” of actualities? Here he underlines his special indebtedness to S. Alexander and C. L. Morgan. The pure phenomenological standpoint of his previous period is no longer satis- factory, as it leads to the deepening of the event/object polarity with the actual occasion/eternal object polarity. On the one hand, the phenom- enological continuous transition is so to speak atomized in ontological units of experience (“epochs”); on the other, the quasi-Platonic notion of eternal object embodies general potentialities. Moreover, the axio- matization of the process of actualization asks for a threefold immanent “principle of limitation” working together with a transcend- ent-immanent “Principle of Concretion”—God—grounding value and order in an eventful universe. The discussion of the concept of God occurs thus in a totally dispassionate context, independently of reli- gious or even ethical concerns. What matters more is the “ontological priority” of flux over permanence and the grounding of actuality in a “sea” of potentiality. In any case, SMW constitutes without doubt a major step (not a leap) in Whitehead's conceptual development. 1 1 With that regard, it is well-known that the standard interpretation of the development of his philosophy finds its basis and its major ex- emplifications in two cumbersome pieces of “evidence” allegedly haunting his corpus: on the one hand, the shift to ontological atom- ism and, on the other, the abolition of the category of conceptual reversion. We cannot argue here in detail that neither of these two so-called shifts are actual and that to claim the contrary endangers the achievement of any coherent interpretation of his system or even of its development. They are the product of dubious premises and lead to even more misleading interpretative consequences. As  Introduction 25 Religion in the Making (being the Lowell Lectures of 1926, delivered in King’s Chapel, Boston, and published in Sept. 1926) resumes the sys- tematic task by naming the three “formative elements” implicit in Science and the Modern World: creativity or substantial activity, eternal objects or pure possibilities, and God or the Principle of Concretion. The Timaeus’ categories are obviously still haunting his mind. In any case, it is the concept of religion that is in the hot seat here, both from the perspective of the relativity of first-hand and second-hand experiences (cf. James' Varieties of Religious Experience, 1902) and of the correla- tion between the history of religion and the general history of knowledge. Science and the Modern World—and, to a lesser extent, Religion in the Making—were (and still are) well-sold books. Due to the topics they address and the treatment they accord them, they have usually been acclaimed by critics and welcomed by the general public as well as scholars. Partly historical and partly common-sensical, they could easily find an open-minded audience in Boston. Nevertheless, it is fair to rec- ognize that, in comparison to Process and Reality (1929), these works were conceptually timid, simply because Whitehead had not yet thought his way to a coherent system. The main damper impeding his speculations was his atavistic Platonism, itself induced by his Logicism and his Anglicanism. In other words, both because of his algebraic Lowe says: “Whether the method of higher criticism that biblical scholars applied successfully to the Pentateuch can be applied with comparable hope to an essay in cosmology written by one old man in the 1920s must be doubted” (V. Lowe, Alfred North Whitehead, op. cit., II, p. 221). Suffice it to say that first, epochality does not amount to atomicity and that discontinuity does not replace conti- nuity in his system (continuity is now understood in a contiguist manner); second, without reversion creativity is equivalent to sub- stantial transformation. Both matters are transcendental: at one point, Whitehead left the question of the conditions of possibility of genuine eventfulness in brackets; later on, he made them explicit. See “Créativité et réversion conceptuelle” in Michel Weber et Diane d’Eprémesnil (sous la direction de), Chromatikon. Annuaire de la philosophie en procès—Yearbook of Philosophy in Process, Louvain- la-Neuve, Presses universitaires de Louvain, 2005, pp. 159-174. 26 Michel Weber training and his Christian education, he was heavily subjected to the creed of the time: creationism (not in the contemporary meaning of the word). Creation is a making not a happening; it is poietic, not praxic.1 It remains however of the highest importance to assess that conceptual reticence in order to understand Process and Reality's drive. All the more so if one does not accept the thesis of the uttermost importance of the Gifford Lectures to understand what is at stake for their author: SMW (together with AI) become then the loci of the revelation of his late worldview. An excellent introduction to Whitehead's Weltanschauung in general, and his epistemology in particular, can be found in his Barbour-Page Lectures of 1927, published under the title of Symbolism, Its Meaning and Effect.2 Symbolism is noteworthy mainly for its introduction of Whitehead’s mature analysis of sense-perception. Our experience, he claims, has three main modes, “each contributing its share of compo- nents to our individual rise into one concrete moment of human experience” (S 17). Two of these modes are perceptive, and the third one names the interplay between the former. The goal is to save “ap- pearance” and “being,” opinion and science. In respect to “pure (sense- )perception”3 or “direct recognition,”4 the philosopher distinguishes “causal efficacy” and “presentational immediacy,” both constituting an objectification of the mundane tissue. On the one hand, in “perception in the mode of causal efficacy,” we “conform to our bodily organs and to the vague world which lies beyond them” (S 43). In other words, we 1 See Michel Weber, “Concepts of Creation and Pragmatic of Cre- ativity,” Wenyu Xie, Zhihe Wang, George Derfer (eds.), Whitehead and China, Frankfurt / Lancaster, Ontos Verlag, 2005, pp. 137-149. 2 The conclusions of S are synthetized in PR, mainly on pp. 117-125 and 168-183. Although PR contains the key to Whitehead’s concep- tual revolution, its study will probably be fruitful only if it comes after the contemplation of less technically dense material. Besides S, FR, AE and MT, Price’s Dialogues are highly recommended (and it is a very interesting question, indeed, to determine why exactly some scholars have ridiculed that work). 3 See, e.g., S 5, 40 and cf. also 17, 20, 53-56 and PR 168. 4 S 7 and passim; PR 65, etc.  Introduction 27 undergo the pressure of an external world which is both determined and past (S 44, 50, 55 and PR 178). That heavy and primitive experi- ence (S 44) brings to the fore the meaning of our embodiment (the “withness of the body,” as he will later call it), which is to root us deeply in the World. On the other hand, “perception in the mode of presentational immediacy” delivers a clear and distinct image of the contemporary world. An instantaneous cut-out presentifies (i.e. renders present) reality as an extensive pattern: determined items localized in a spatio-temporal continuum. This projection, in our present, is achieved with the (past) data delivered by causal efficacy. Its paradigm is sight and the coldness of its objectification: to locate is the act of sight itself. The intrinsic natural processuality is here obliterated; the World be- comes stiff and lifeless, a mosaic of qualities spread out in front of an acosmic subject.1 None of the two pure modes can be judged true or false, only their confrontation could: Aristotle saw it already, truth and falsehood are not “in” things, but in the synthesis made by the mind. In order to explain perceptual errors and other, more positive, degrees of freedom humans can enjoy with facts, Whitehead introduces “symbolic reference,” which is the conscious synthetic activity whereby the two pure modes are “fused into one perception” (S 18). To mistake a square tower for a round one is to misinterpret what is actually given to us: although what is seen is undoubtedly a roundish object, the tower is indeed square and this fact cannot but be conveyed by causal efficacy. “Direct experience is infallible. What you have experienced, you have experienced” (S 6). The mistake lies in the conscious judgment claiming that this tower is round. His answer to Hume (and Descartes) is thus the following. Although it is with good reason that the Scot criticizes perception in the mode of presentational immediacy, his reduction of all possible perception to sensory perception (restricted to the five senses) is mistaken. In sum: conscious perception is understood as “the 1 “Une mosaïque de qualités étalée devant un sujet acosmique” (Maurice Merleau-Ponty, Phénoménologie de la perception, Paris, NRF Éditions Gallimard, 1945, p. 359). Cf. Hans Jonas, Philosophical Essays. From Ancient Creed to Technological Man, Chicago, University of Chicago Press, 1974. 28 Michel Weber symbolic interplay between two distinct modes of direct perception of the external world.”1 The Aims of Education (1929) gathers addresses given between 1912 and 1928 (it actually recaptures most of the essays published in The Organisation of Thought, Educational and Scientific, 1917). The Preface summarizes the stakes: “The whole book is a protest against dead knowledge, that is to say, against inert ideas.” According to Whitehead, “education is the acquisition of the art of the utilisation of knowledge” and such an art necessarily involves the uncompromising awareness of duty (that “arises from our potential control over the course of events”) and reverence (which is “this perception, that the present holds within itself the complete sum of existence, backwards and forwards, that whole amplitude of time, which is eternity”2). Accordingly, he spells the rhythm of education in three phases: wild Romance, efficacious Preci- sion and visionary Generalisation. Process and Reality (being the Gifford Lectures of 1927–1928, pub- lished in December 1929)3 disrupts RM’s threefold Platonic framework by reorienting it around the concept of “creativity.” Although Process 1 “There are, in this way, two sources of information about the external world, closely connected but distinct. These modes do not repeat each other; and there is a real diversity of information. Where one is vague, the other is precise: where one is important, the other is triv- ial. But the two schemes of presentation have structural elements in common, which identify them as schemes of presentation of the same world. There are gaps, however, in the determination of the correspondence between the two morphologies. The schemes only partially intersect, and their true fusion is left indeterminate. The symbolic reference leads to a transference of emotion, purpose, and belief, which cannot be justified by an intellectual comparison of the direct information derived from the two schemes and their ele- ments of intersection” (S 30-31; see PR 122-123). 2 Cf. OT 9-10 and 28 or AE 4 and 14. 3 Whitehead sent the last proofs to Macmillan on Aug. 13, 1929. On Nov. 4 he wrote to his son North that he didn't expect a good recep- tion from philosophers. We infer that since it was published in 1929, it had to be Nov. or Dec., together with FR. (See Lowe’s bibli- ography, Vol. II, 252 and 339.)  Introduction 29 and Reality constitutes Whitehead's most imposing work, undoubtedly the acme of his speculations, it was—and is still—badly received and drastically misunderstood. Actually, Whitehead wrote to his son North: “I do not expect a good reception from professional philosophers.”1 As a matter of fact, the Lectures were a debacle, and the book itself is usually fragmented in order to make it sizeable for hurried readers. It constitutes of five strictly interdependent parts: I. “The Speculative Scheme;” II. “Discussions and Applications;” III. “The Theory of Pre- hensions;” IV. “The Theory of Extension;” and V. “Final Interpretation.” Part One includes the famous “categoreal scheme” that is “practically unintelligible” unless studied along with the rest of the book. Part Two (which is the weakest) mainly studies the Classics and Kant from the perspective of its reformed subjectivism. Part Three analyses “geneti- cally” the coming into existence of new actualities. Part Four analyses “coordinately” the being of actualities (and defines straight lines with- out reference to measurement). Part Five reinterprets the ontological system so far adumbrated, starting with the rebalancing of the God/World relationship. The ill-success of Process and Reality seems to have suggested a re- newal of the expository style of Science and the Modern World. Adventures of Ideas (1933) elucidates the main categories of Process and Reality with the help of a vast picture of the major ideas haunting civilizations. We have here not only a philosophy of history emphasiz- ing the concept of persuasion, but also an assessment of the impact of the scientific worldview on European culture and a renewed exposition of the ontology of process. According to the philosopher, a civilized society is to exhibit the qualities of Truth, Beauty, Adventure, Art, and Peace. The Function of Reason—being the Louis Clark Vanuxem Foundation Lectures delivered at Princeton University, March 1929—constitutes Whitehead’s most valuable meditation on the complementary topics of Darwinian evolution and Jamesean Pragmatism. It is structured in a remarkably dialectic way: it first introduces the pragmatic function of 1 See Lowe's A.N. Whitehead, op. cit., II, p. 252. 30 Michel Weber reason, then its theoretical function, and lastly its (hyperdialectical1) theoretico-pragmatic one. The first definition Whitehead gives of the function of Reason is “to promote the art of life” (FR 4). Although this is promptly reformulated as “the direction of the attack on the envi- ronment,”2 the philosopher remarks that life should not be equated with survival as such: mere persistence is nothing but death.3 Life should be approximated by three concepts that will be evoked again with the introduction of the “creative advance of nature”: self- enjoyment, creativity and aim. But there is a second, equally important, function of reason: the speculative one, which is far less focused on immediate issues and attempts to grasp the overall picture. It is a “god- like faculty which surveys, judges and understands” (FR 9). The pragmatic function is rooted in our animal life (this being not a deroga- tive statement), the speculative one in civilization. The former promotes life in all its dimensions; the latter, science and its disinte- rested quest. However, neither life nor science has the last word in Whitehead’s Victorian optimism: Ulysses and Plato pave together the way for James Watts’ (1736–1819) techno-science. With technoscience, a synergy is established between the archaeological propensity of speculative systematization and the consequentialism of pragmatic thought. In a somewhat Kantian manner, Whitehead insists on the complementarity of the two functions: methodology and direct obser- vation derive from the practical side4 while the global imaginative 1 “La mauvaise dialectique commence presque avec la dialectique, et il n’est de bonne dialectique que celle qui se critique elle-même et se dépasse comme énoncé séparé; il n’est de bonne dialectique que l’hyperdialectique” (Maurice Merleau-Ponty, Le Visible et l'Invisible. Suivi de Notes de travail. Texte établi par Claude Lefort, accompagné d'un avertissement et d'une postface, Paris, Éditions Gallimard, 1964, p. 129). 2 “The primary function of Reason is the direction of the attack on the environment” (FR 8). 3 “The art of persistence is to be dead” (FR 4). 4 “Each methodology has its own life history. It starts as a dodge facili- tating the accomplishment of some nascent urge of life. […] The birth of a methodology is in its essence the discovery of a dodge to live” (FR 18).  Introduction 31 standpoint needed to pilot it and the emphasis upon novelty1 are theo- retical. Modes of Thought (1938) gathers together Whitehead’s last lectures, spread over the years 1924–1938. Their main object is to bring to the fore the presuppositions and oversimplifications that underlie abstrac- tions, whether they be everyday, commonsensical patterns of thought or elaborate scientific systematizations. Whitehead shows, with the help of the concepts of importance, interest, discrimination and per- spective, that there is a continuous gradient from the infinite unity or connexity of all events to the individual, finite, selectiveness of enjoy- ment of conscious actualities. By the same token, he insists on the difference between intuition, thought, and language and contrasts the sheer, vibrant disclosure of stubborn facts with their symbolization in science, philosophy, poetry and mysticism. Ideals can mask the con- crete, well placed abstractions never. “Autobiographical Notes,” “Immortality,” and “Mathematics and the Good,” first published in the Schilpp volume devoted to The Philosophy of Alfred North Whitehead (1941; reprinted in his 1947 Essays in Sci- ence and Philosophy), constitute his last major publications. All three make the same plea for relativism in PR’s reformed sense of the term and for its direct correlates pattern and rhythm. First of all, Whitehead makes clear that his thought has always been anchored in his vivid knowledge of history and in plain conversation, both common-sensical and technical, with colleagues, students and friends. Second, the Uni- verse is understood as the interplay between two “Worlds,” the World of Active Creativity and the World of Timeless Value. The former is the World of origination of patterns of assemblage that nevertheless devel- ops Enduring Personal Identity. The latter is timeless and immortal, but it nevertheless seeks Realization. In sum: neither finitude nor infinitude 1 “Reason is the organ of emphasis upon novelty. It provides the judg- ment by which it passes into realization in purpose, and thence its realization in fact” (FR 20). “Fatigue is the antithesis of Reason” (FR 23). 32 Michel Weber are self-supporting; fact and value require each other—and “exactness is a fake.”1 2. Whitehead’s Legacy It is well known that until recently Whitehead has kept a fair visibility only in Protestant natural theology and mainly in the United States. There is however nowadays a (re-)discovery of Whitehead in philo- sophical and scientific circles: below, we propose a brief overview of the Whiteheadian legacy and list a few of the most recent promising development in Europe, Asia and Africa. 2.1. United States The propagation of Whiteheadian organic philosophy outside Harvard was first due to Henry Nelson Wieman (1884–1975), who did not study under Whitehead but introduced, as early as 1926, the standpoint of Religion in the Making to Chicago’s Divinity School, whose tradition was, from its founding in 1890 by William Rainey Harper (1856–1906) until the early 1950s, empirical (or natural) theology. There has been, as a result, a steady interest in Whitehead among theologians, first at the University of Chicago, later at the Claremont School of Theology (Claremont, California). Charles Hartshorne (1897–2000), Daniel Day Williams (1910–1971), Bernard MacDougall Loomer (1912–1985)— who is likely to have coined, for better or for worse, the term “process thought”—and Bernard Eugene Meland (1899–1993) rank among the first wave of these impressive Whitehead-inspired scholars. In the six- ties emerged John B. Cobb, Jr. (1925–) and Schubert M. Ogden (1928–). Cobb’s Christian Natural Theology (1965/2007) remains a landmark in the field. The journal Process Studies was created in 1971 by Cobb and Lewis S. Ford (1933–); the Center for Process Studies was established in 1 “Immortality,” p. 19; reprinted in ESP 96 and in IS 267; cf. D 176 and ESP 104. Elsewhere he advised “seek simplicity and distrust it” (CN 163; cf. PNK 76).  Introduction 33 1973 by Cobb and David Ray Griffin (1939–) in Claremont. The result of these developments was that Whiteheadian process scholarship has acquired, and kept, a fair visibility only in North-American natural the- ology. Whitehead’s philosophical legacy was far less unified, though it too was a lively one. Willard Van Orman Quine (1908–2000), the most famous of Whitehead’s students with Bertrand Russell—and who be- longs after all to the formative phase of a new (analytical) ontology— did not follow the speculative path of his mentor. Neither did Paul Weiss (1901–2002), who apparently finally repudiated completely the philosophy of organism. Other past students like William Ernest Hock- ing (1873–1966), Filmer Stuart Cuckow Northrop (1893–1992), Suzanne Katherina (Knauth) Langer (1895–1985), Victor Augustus Lowe (1907–1988), Joseph Gerard Brennan (1910–1977), Max Harold Fisch (1901–1995) or Allison Heartz Johnson (1910–1973) never kept the argumentative pressure high enough—or federated their efforts en- ough—to promote the ideas of their teacher the way theologians did. Neither did prominent philosophers like Wilbur Marshal Urban (1873– 1952), Sydney Ernest Hooper (1880–1966), Lizzie Susan Stebbing (1885–1943), William Armistead Christian (1905–1997), Mili apek (1909–1997), Ivor Leclerc (1915–1999), William Norris Clarke (1915–), Nathaniel Morris Lawrence (1917–1986), George Louis Kline (1921–), Walter Eliott Stokes, S.J. (1923–1969) or Robert Monroe Palter (1924–). Founded in 1966, the Society for the Study of Process Philosophies (http://www.processphilosophies.org) was one of the first satellite orga- nizations of the American Philosophical Association. The SSPP holds periodic meetings in conjunction with each of the divisional meetings of the American Philosophical Association, as well as at the annual meeting of the Society for the Advancement of American Philosophy. The SSPP is presently coordinated by Jude Jones with the associate director Brian G. Henning. 34 Michel Weber 2.2. Europe From a European perspective, there was a very significant and often early Whiteheadian influence on the works of outstanding scholars like Henri Bergson (1859–1941), Émile Meyerson (1859–1933), Louis Cou- turat (1868–1914), Jean Wahl (1888–1974), Robin George Collingwood (1889–1943), Philippe Devaux (1902–1979), Hans Jonas (1903–1993), Dorothy M. Emmet (1904–2000), Maurice Merleau-Ponty (1908–1961), Enzo Paci (1911–1976), Charlie Dunbar Broad (1887–1971), Wolfe Mays (1912–2005), Ilya Prigogine (1917–2003), Jean Ladrière (1921– 2007), Gilles Deleuze (1925–1995), Wolfhart Pannenberg (1928–) and Reiner Wiehl (1929–), but all have kept their own speculative trajectory. (Russell’s case is again too complex to be addressed here.) Louvain’s Center for Metaphysics maintains Whiteheadian archives, established by Jan Van der Veken (1932–) in 1977 with the help of Claremont’s Center for Process Studies and now directed by André Cloots (1948–); it is also the host of the European Society for Process Thought, created November 10th 1978, on the occasion of the bestowal of a honorary doctorate on Charles Hartshorne.1 2.3. Recent Evolution Recent years have seen the revival of the interest in Whitehead’s phi- losophy, either directly (through the interpretation of Whitehead secundum Whitehead) or indirectly, because of debates around prob- lematic epistemological knots (such as interpretational problems in quantum mechanics or in relativity, and chronic difficulties such as the so-called mind-body problem), on the occasion of the reassessment of “great classics” such as Locke, Hume and Kant, or because of some currently fashionable work, e.g. in France, through Gabriel (de) Tarde (1843–1904), Gilbert Simondon (1924–1989) and Gilles Deleuze (1925– 1995). Furthermore, Whitehead’s anticipating insights on the conver- 1 Centrum voor Metafysica en Wijsgerige Antropologie, Hoger Instituut voor Wijsbegeerte, 3000 Leuven, Belgium; see www.espt.de.  Introduction 35 gence of fields like “gender studies” and “sociology of science” remain fascinating: Except for plain, overmastering reasons connected with the necessary efficiency of Government, it is a crime against Liberty deliberately to deprive any portion of the population of possibilities of political action. That such overmastering reasons for limitation of political functions do exist in many states, perhaps in all states, I am not concerned to deny. They may arise when there is a cleav- age in the population produced by inferiority of race, inferiority of civilization, or by deficiency of goodwill.1 Here is a brief sketch of the recent major international initiatives. The Japan Society for Process Studies was established on December 8, 1979. Its current president is Haruo Murata (Aomori Public College). The secretariat of the JSPS is located at Hitoshi Hongo's office at Tokyo Denki University.Tokiyuki Nobuhara (who is also chairing the East-West Process Studies Project since 1985) acts as project director. The JSPS fosters three study groups—in Tokyo (dir.: Chuichiro Hirose, Canon University), in Kyoto (dir.: Eiko Hanaoka, Nara Industrial University), and in Nagoya (dir.: Yasuto Murata, Nagoya Ryujo Junior College)—and, since 1985, a journal, Process Thought (editor: Yutaka Tanaka, Sophia University). Almost all of Whitehead’s works have been translated and published by Shoraisha edition in Kyoto. On September 2007, the JSPS had its 29th Annual Convention at Doho University, Nagoya with a special symposium on “Whitehead and Peace” as its focus. Isami Nagami (Nagoya Ryujo Junior College), Tsugiko Sakai (Tokushima Bunri University), Shigeyuki Itoh (Kyushu Industrial University) were speak- ers, with Tokiyuki Nobuhra (Keiwa College) and Masaharu Hishiki (Doho University) playing the roles of comentator and president. Hiro- shi Endo (Waseda University emeritus) delivered a keynote lecture on “Whitehead's Metaphysics.” Among JSPS’ recent publications, one finds a collection of essays delivered at the 30th Anniversary of Japan Society for Process Studies, held at Aomori Public College, in October 2008: 1 Alfred North Whitehead, “Liberty and the Enfranchisement of Wo- men” [Cambridge, Cambridge Women’s Suffrage Association, 1906], reprinted in Process Studies 7/1, 1977, pp. 37-39, p. 38. 36 Michel Weber Haruo Murata (ed.), Whitehead and Ethics in the Contemporary World: For Sustainability and Common Good (Kyoto, Shoraisha/The Japan Soci- ety for Process Studies, 2010). The Australasian Association for Process Thought (www.processthought.org) was formed in 1996 by process philosopher and theologian Greg Moses and computer scientist Peter Farleigh, with support from biologist and writer Charles Birch and humanities profes- sor Wayne Hudson. The aim of the organisation is to promote the study of the process-relational thought of Alfred North Whitehead and Charles Hartshorne in the Antipodes. Membership consists of philosophers, scientists, medics, psychologists, clergy, students, and other interested scholars from all over Australia, New Zealand and Papua New Guinea. In June 2000 the AAPT launched an on-line peer-reviewed journal called Concrescence (www.concrescence.org) and in 2005 members of AAPT created a new peer reviewed on-line journal: Cosmos and History: The Journal of Natural and Social Philosophy (http://www.cosmosandhis- tory.org). Learned papers are invited on all subjects addressing the problems and issues in process-relational metaphysics. The journals provide a forum for exploring a broad range of issues in this speculative or revisionist field, but not ignoring critical and analytical methods: from the philosophy of science to theology, from environmental ethics to politics, from historical analyses to contemporary issues. The Whitehead Society of Korea (http://whitehead.or.kr/) was created in 1997 after a research stay of Wang Shik Jang in Claremont. The WSK held its first conference at Yonsei University in Seoul on March 29, 1997. It is currently chaired by Chang-Ok Mun. The Chromatiques whiteheadiennes scholarly society was created in January 2000 by Michel Weber. In 2006 it has been incorporated as a non-profit organization that regroups the Chromatiques, the Whitehead Psychology Nexus and the European William James Project: the Centre for Philosophical Practice “Chromatiques whiteheadiennes”. The Chro- matiques network itself intends to bring together research on the different aspects, nuances and implications of Whitehead's thought.  Introduction 37 Since 2002, the network has fostered in Paris 1-Panthéon Sorbonne research seminars on Whitehead’s organic philosophy. The Chromati- kon Yearbook publishes the main results of this work and also offers critical studies and reviews in Whiteheadian and related fields. It com- plements the monographs and proceedings published in Ontos' “Chromatiques whiteheadiennes” and “Process Thought” series. Since December 2007, the Centre has furthermore activated its own publish- ing company—Les Éditions Chromatika—with nine volumes presently available. See www.chromatika.org. The Whitehead Psychology Nexus scholarly society was created in October 2000 by Michel Weber. It is an international open forum dedi- cated to the cross-examination of Whitehead's “process” philosophy and the various facets of the contemporary psychological field. It seeks to encourage psychology in a Whiteheadian atmosphere and White- headian scholarship informed by psychology. Openness means here that no philosophical or psychological system of thought is a priori ex- cluded, provided that they allow discussion in a Whiteheadian spirit. It has published three collective volumes.1 See www.chromatika.org. The International Process Network (IPN) was created in Claremont in January 2001. It is a global network for process-relational philosophies governed by a multi-cultural and interdisciplinary board. IPN’s purpose, as stated in its bylaws, is “to support, generate and disseminate an international discourse on the meaning and implications of process thought across academic disciplines and conflicting truth-claims, and in relation to the entire community of life and the cosmos.” Membership in IPN is available to individuals and organizations who are interested 1 Searching for New Contrasts. Whiteheadian Contributions to Contem- porary Challenges in Neurophysiology, Psychology, Psychotherapy and the Philosophy of Mind, Frankfurt am Main, Peter Lang, 2003; The Roar of Awakening. A Whiteheadian Dialogue Between Western Psychotherapies and Eastern Worldviews, Frankfurt, Ontos Verlag, 2009; Process Approaches to Consciousness in Psychology, Neuro- science, and Philosophy of Mind, Albany, New York, State University of New York Press, 2009. 38 Michel Weber in understanding, teaching, developing, applying, promoting or sup- porting process. See www.processstudies.org. In 2001, the University of Liège has revived its old tradition of White- headian scholarship. It started in the thirties, under the leadership of Philippe Devaux (1902–1979), who had attended Whitehead’s classes.1 When Paul Gochet took over his professoral charge, there was a slight shift towards Whitehead’s student, W.V.O. Quine. With François Beets, Whitehead is back as a main departemental actor. It is thanks to Beets that the first Chromatiques conference was organized in Liège in 2001 and that, more recently, a common research project was concluded in 2008 with the Bulgarian Academy of Science. Émeline Deroo currently works under his supervision on a Ph.D. dissertation on Whitehead and Simondon. On the other hand, Bruno Leclercq regularly lectures on the Principia Mathematica. The Groupe d'Études constructivistes at the Université libre de Bruxelles, created circa 2002 by Isabelle Stengers, focuses on contem- porary philosophical issues with the help of Spinoza, James, Whitehead, Deleuze, Dewey, Foucault, Haraway and Latour. A Research Chapter for Applied Process Thought was created in 2002 in the University of St. Andrews by Mark Dibben. The Chapter has since then moved to the National University of Ireland, Maynooth, under the leadership of the late Thomas A. F. Kelly, and subsequently under Wil- liam Desmond Jr. Dibben is also a member of the Joseph Needham Center for Complex Processes Research, headed by Arran Gare at Swimburne University (Australia). Unlike many process research centers, whose focus is predominently Whiteheadian, the CCPR is ac- comodating of a range of process philosophies and has a focus on ecological economics and sustainability issues. It is the most active 1 Philippe Devaux, La Cosmologie de Whitehead. Tome I, L'Épistémologie whiteheadienne, édité par Thibaut Donck et Michel Weber, Louvain- la-Neuve, Éditions chromatika, 2007. Cf. Paul Gochet, “Philippe Devaux, sa vie, son oeuvre,” Bulletin de la Classe des Lettres, Bruxelles, Académie Royale de Belgique, Tome XIX, 2008, pp. 181- 196.  Introduction 39 center of its kind in Australasia with its own refered journal Cosmos and History. Since his move from Scotland to Australasia, Dibben has taken on the Executive-director role of the International Process Network, to which all the centres in this synopsis are affiliated. The IPN’s own asso- ciated journal Concrescence is also based in Australia under the editorship of Peter Farleigh. Thanks to Zhihe Wang's intercession, no less than fourteen centers devoted to process thought were open recently in the People's Republic of China: Beijing Center for Process Philosophy (2002), Wuhan Center (Process Philosophy, 2002), Xian Center (Process Philosophy, 2003), Beijing Center for Process Thinking (2004), Yancheng Center (Process Education, 2005), Suzhou Center (Process Philosophy, 2005), Zhanjiang Center (Process Education, 2005), Hangzhou Center (Process Theology, 2005), Shangdong Center (Process Psychology, 2005), Tianjin Center (Process Education, 2005), Shenyang Center (Process Ecology, 2007), Heilongjiang Center (Process Philosophy, 2007), Guilin Center (Con- structive Postmodern Culture, 2006), and Shanghai Center (Sustainable Urbanization, 2007). Some of them were open on the occasion of a conference co-organized with Claremont’s China Project and the Insti- tute for Postmodern Development of China. The topics included, e.g., philosophy, sustainable urbanization, education reform, the dialogue between science and spirituality, social responsibility in business, land and social justice, and postmodern law, management.1 1 “Whitehead and China in the New Millennium,” Beijing, June 17-20, 2002; “Marxism and constructive Postmodernism,” Wuhan, June 21-22, 2002; “Educational Reform,” Claremont, November 1-4, 2003; “Marx and Whitehead,” Beijing, April 4-6, 2004; “Theoretical Innovation,” Beijing, May 30-31, 2004; “Philosophy of Culture,” Harbin, May 30-31, 2004; “Science and Faith in Global Context,” Beijing, December 28-29, 2004; “Higher Education Reform,” Yan- cheng, April 6-10, 2005; “Faith, Science and Environment,” Beijing, August 7-8, 2005; “Science and Spirituality in the Postmodern World,” Wuhan, October 11-13, 2005; “Toward a Sustainable Ur- banization,” Suzhou, October 14-17, 2005; “Sustainable Urbanization and Ecological Civilization,” Shanghai, October 18-19, 2005; “Land and Social Justice,” Beijing, October 21-22, 2005; “Phi- losophy and Management,” Beijing, October 22-23, 2005; “China’s 40 Michel Weber The Polish Whitehead Metaphysical Society was founded in 2003 and registered in October 2005. It was founded by a group of twenty Polish philosophers in order to support the development of Whiteheadian metaphysics. Its work takes place in four workshops: Philosophy of Nature, Interreligious Dialogue, Philology, Cognitive Science. Students founded three Process Circles at their Universities in Krakow, Lublin, Katowice. The Society organizes a weekly seminar, an annual confer- ence in May1 and publishes the Studia Whiteheadiana (issue 1, 2003; 2, 2006; 3, 2008). Since 2009, it is the main organizer of the European Summer School on Whitehead's philosophy in Katowice (2-7 August 2010). The contact person is: Bogdan M. Ogrodnik (Silesian Botanical Garden), bogrod@interia.pl; http://towarzystwo.panewniki.pl/english. The Hungarian and Central European Whitehead Society (Budapest) was established in 2003. It organizes monthly discussions, inviting not only philosophers, but also experts from areas like theology, informa- tics, psychology, sociology, history, art etc. Two members of the society translated Process and Reality (published by Typotex, 2001): László Fórizs and Gábor Karsai. In 2007 the Concept of Nature was published in Hungarian (Typotex, 2007, translated by Levente Szabados) and Modernization,” Claremont, California, December 16-18, 2006; “Postmodern and Enlightenment,” Beijing, April 7-8, 2007; “Law, Morality, and Politics from a Constructive Postmodern Perspective,” Beijing, July 8-9; “Social Responsibility in Business and Harmonious Society,” Tianjin, July 14-15; “Science & Technology Ethics and Business Ethics,” Dalian, July 16-18; “Process Thinking and Curricu- lum Reform,” Yantai, Shandong, July 19-20; “Philosophy: its Basic theory and problems,” Jilin, July 25-29; “Constructive postmodern- ism, Marxism and Ecological Civilization,” Claremont, October 26- 28, 2007. 1 “Polish Studies of Whitehead's Philosophy,” 2003; “Process Philoso- phy in the Past and Today,” 2004; “The Dynamism and Order of the Real World,” 2005; “On the Nature of Human Time” (co-organized with the Whitehead Psychology Nexus), 2005; “Problems Concern- ing Process Categories,” 2006; “Problem of God from Process Perspective,” 2007; “Philosophical Basis of Inter-religious Dialogue,” 2008, “Process Philosophy and Philosophy of Nature,” 2009; “From Organism to Society. Whitehead and Modern World,” 2010.  Introduction 41 Studies on process philosophy were published (Process and Adventure, Veszprém, 2006, edited by Ella Csikós and Gábor Karsai). Every sum- mer a “Whiteheadian camp” takes place at lake Balaton, with lessons and cultural programs. Web site: http://whitehead.fw.hu/; e-mail: in- fo@whitehead.hu. The Whitehead Research Project (WRP), established by Roland Faber in 2007, heralds the forthcoming Whitehead Research Institute. It is dedicated to the research of, and scholarship on, the texts, philosophy and life of Alfred North Whitehead. It explores and analyzes the rel- evance of Whitehead’s thought in dialogue with contemporary philosophies in order to unfold his philosophy of organism and its con- sequences for our time and in relation to emerging philosophical thought. Of particular interest is the investigation of the emergence of Whitehead’s philosophy in the context of British and American pragma- tism, its relation to Continental philosophy and the analytic tradition, the relevance of his thought in the discourse of post-modern paradigms of deconstruction and post-structuralism, and its creative impulse for developing process philosophies.1 Additionally, following Whitehead’s own inclination to reach beyond European modes of thought, WRP seeks to extend its horizon of research by fostering similar conversa- tions with strains of Indian and East Asian thought, thereby exhibiting de facto mutual influence—e.g., with the Kyoto School of Buddhist philosophy. The WRP hosts a yearly international conference in Clare- mont on Whitehead and his relation to contemporary scholarship, which includes speakers such as Judith Butler, Isabelle Stengers, Steven Shaviro, and Graham Harman. Forthcoming titles from the WRP’s Con- temporary Whitehead Studies series are expected to appear in 2011. The Bulgarian Center for Process Studies was officially established on November 2007 with the help of Claremont’s CPS. It is a a non-profit 1 See Roland Faber and Andrea M. Stephenson, eds., Secrets of Becom- ing: Negotiating Whitehead, Deleuze, and Butler, New York, Fordham University Press, 2010; Roland Faber, Henry Krips, and Daniel Pet- tus, eds., Event and Decision: Ontology and Politics in Badiou, Deleuze, and Whitehead, Cambridge, Cambridge Scholars Publishing, 2010. 42 Michel Weber organization. Its president is Assoc. Prof. Dr. Vesselin Petrov; the vice- president is Assist. Prof. Dr. Rosen Lutskanov; and the secretary is As- sist. Prof. Dr. Stefan Dimitrov. The Center has established synergies with its Romanian, Hungarian and Polish conterparts and with the Chromatiques whiteheadiennes and Liège university (Belgium). It is one of the co-organizers of the European Summer School on Whitehead's philosophy in Katowice, Poland. E-mail: bulgcenterprocessstud- ies@mail.bg. In April 2008 a Whiteheadian research center was opened in the Fac- ulty of Letters and Social Sciences of the “Constantin Brancusi University” (Romania). Its Honorary President is Bertrand Saint-Sernin, professor emeritus of Paris IV–Sorbonne and doctor honoris causa of CBU. Its President is Prof. Adrian Gorun, Ph.D., Rector of CBU. The center, has now become an Institute of research that operates at the level of the university. It fosters a globalist approach in the field of re- search and will focus on strengthening the academic relations with the other Whiteheadian centers in Europe and USA. E-mail: onasys@utgjiu.ro. In Africa, there has been a constant interest in Whitehead since the seventies with the works of Tshishiku [Tharcisse] Tshibangu, who found his main inspiration in Whitehead, Yves Congar and Jean Ladrière.1 Joseph Mabika Nkata,2 Alphonse Ngindu Mushete3 and David Ongombe 1 See Mgr Tshishiku [Tharcisse] Tshibangu, Théologie positive et théolo- gie spéculative, position traditionnelle et nouvelle problématique, Louvain, Publications universitaires, 1965; La théologie comme sci- ence au XXe siècle. Préface par Marie-Dominique Chenu. Postface par J. Ladrière, Kinshasa, Presses Universitaires du Zaire, 1980. 2 Joseph N. Mabika, “La résurrection de la métaphysique en Afrique noire,” in Dimandja Eluy’a Kondo et Mbonyinkebe Sebahire (sous la direction de), Théologie et cultures. Mélanges offerts à Mgr Alfred Vanneste, Louvain-la-Neuve, Nouvelles Rationalités Africaines, 1988, pp. 401-427. 3 Alphonse Ngindu Mushete, Les thèmes majeurs de la théologie afri- caine, Paris, Éditions L’Harmattan, 1989.  Introduction 43 Talhuata1 are continuing Tshibangu’s initial exploration of the bridges between organic/process philosophy and African theologies and world- views. A Centre Monseigneur Tshibangu. Métaphysiques—Sciences— Théologies, planned back in 2005 in the Université de Lubumbashi, R.D. Congo, has eventually been opened while other centers are now operating in Kinshasa university and in Kinshasa catholic university. In January 2010, German Whiteheadian scholars have federated their efforts by creating the Deutsche Whitehead Gesellschaft, housed by the Institut für Philosophie of Heinrich-Heine-Universität Düsseldorf that is currently chaired by Helmut Maaßen (http://whitehead-gesellschaft.de). The Society intends to foster research on all aspects and nuances of Whitehead’s thought, historically as well as systematically. His work will be undogmatically related to other philosophical traditions and the interdisciplinary relevance of process thought will be explored. German Process philosophy in the Whitehead tradition will be fostered and deepened. The founding members are: Stascha Rohmer (Humboldt University, Berlin), Spyridon Koutroufinis and Hans Poser (Technische University, Berlin), Christoph Kann, Helmut Maaßen and the three doc- toral students Aljoscha Berve, Tanja Kosubek and Dennis Soelch (Düsseldorf University), Reto Luzius Fetz and Sebastian Ullrich (Eich- stätt University), Tobias Müller (Frankfurt University), Regine Kather (Freiburg University), Barbara Muraca (Greifswald University), Michael Welker, Reiner Wiehl (Heidelberg University), Maria-Sibylla Lotter (Kon- stanz University), Robert Spaemann, Mateusz Pychynski (Munich University), Franz Riffert, Hans-Joachim Sander (Salzburg University), Michael Hampe (Zürich University), Pierfrancesco Basile (Bern Univer- sity). In July 2010, the Centre for Philosophical Practice “Chromatiques whiteheadiennes” has organized its first Applied Process Metaphysics Summer Institute. This project, that goes back to the creation of the 1 B. Bourgine, D. Ongombe et M. Weber (sous la direction de), Regards croisés sur Alfred North Whitehead. Religions, sciences, politiques, Frankfurt, Ontos Verlag, 2007. 44 Michel Weber Centre itself (2006), had long been postponed by lack of adequate insti- tutional support. 3. The Urizen of Whiteheadian Scholarship Eternals! I hear your call gladly. Dictate swift winged words, and fear not To unfold your dark visions of torment. William Blake, The Book of Urizen [1794], Preludium For a full-fledged Whiteheadian process thinker, the future status and applicability of process modes of thought is unknown in principle. And we should gladly rejoice at this state of affairs because the very mean- ing of our lives depends upon this existential elbow-room. We live in an open universe that only partially allows us to foresee events, all the more so if they belong to the highest level of complexity known to us: our common—intersubjective—existence. Of course, we could take advantage of our knowledge of the past his- tory of Whiteheadian scholarship and of a sharp (and preferably dispassionate) assessment of its current state to anticipate its likely immediate outcome. Such a speculation will not be proposed here. We would indeed need to carefully peruse the history of Whiteheadian scholarship and its contemporary context before being able to frame the most applicable imaginative generalization and such a study is not appropriate for the present context. For one thing, we would need far more space than it is allowed; for another, by doing so we would wager on the bare efficacy of the actors whereas what we need is to trust their creativity and, most of all, their vision. (While the efficacy of the past pushes experience in the furrow of habit, the creativity of the present, lured by some eschatological commitment, re-creates it moment by moment.) Alternatively, we could speculate on the rhythmic development of the world of ideas in the West. There are obviously conceptual rhythms that frame the history of ideas and Whitehead himself would have in-  Introduction 45 sisted that there always will be novel conceptual epochs to come. The well-known contrast between pluralistic empiricism and dualistic ra- tionalism (see for instance the opening chapter of James’ Pluralistic Universe) is a bit too broad to allow the development of an applicable picture in the context of our present discussion. If we consider the last centuries of human thought, the following dialectical movement— displaying a shift of epicentre from Italy to Germany and later to the Anglo-Saxon world (the latter constituting a far more diffuse entity be- cause of its world-wide cultural hegemony)—can be nevertheless identified. Whereas the Renaissance lauded the perfection of static proportions, Baroque art and thought, heir to the Counter-Reformation of 1630–1750, stressed movement, change and growth. The reaction of the Aufklärung was swift: secularization with its requirements of ra- tionality, optimism and progress spread its dogmatic wings over the entire social landscape (remember Foucault’s grand renfermement). With Romanticism, the emphasis returned to feeling, becoming and opacity (or inexhaustibleness: cf. R 15), sometimes even irrationality. Then the positivism of A. Comte and later of the Wiener Kreis (soon to be exported to the USA) constituted a new Kehre, promptly counter- balanced by the first process publications of F. Nietzsche and É. Boutroux, but also of C.S. Peirce, W. James and A.N. Whitehead (not to forget their conceptual kin: H. Bergson). The conclusion could be: pro- cess thinkers can be optimistic because their mode of thought has not yet developed all its potentialities or become generally recognized (al- though science is nowadays totally processual). But they should not be dazzled either: “in its turn every philosophy will suffer a deposition.”1 A more suitable, if not promising, analysis follows the path suggested by Process and Reality’s (1929/1978) seminal definition of speculative philosophy. It could help to understand the next historical move and its conditions of possibility. Before following the path, we need however to 1 Alfred North Whitehead, Process and Reality. An Essay in Cosmology, Cambridge, Cambridge University Press, and New York, Macmillan, 1929. Reprint: New York, Macmillan Free Press, 1969. Corrected edition: Edited by David Ray Griffin and Donald W. Sherburne, New York and London, The Free Press, 1978, p. 7. 46 Michel Weber trace it through the sometimes wild conceptual territory Whitehead has left us to explore. Hence the following three steps: first, a systematic account of Process and Reality’s conception of philosophical speculation; second, its appli- cation to the question of the future status and applicability of process thought; third a complementary specification with the help of White- head’s insistence on duty and reverence. 3.1. Process and Reality’s Definition of Speculative Philosophy The marrow of Whitehead’s understanding of the meaning and signifi- cance of speculative philosophy is expressed in the first two pages of his magnum opus. Unfortunately, Process and Reality’s first section is not as straightforward as one could expect from such a prolegomenal statement and the basic criteria used—coherence, consistency, applic- ability, adequacy and necessity—seem at first reading a bit fuzzy. The reader who has taken the time to tame Whitehead’s vision can however avoid the Charybdis of relativism and the Scylla of dogmatism in his or her interpretation. The twofold leading idea is not extravagant at all: on the one hand, each criteria has a proper weight or “raison d’être” in the argument; on the other, only their togetherness makes sense. We will not go all over again the long argument required to es- tablish this thesis since it has been unfolded elsewhere;1 only a short reminder of its conclusions will suffice here. The main concern should be not to explain away the richness of the picture proposed to us. On the one hand, we need to distinguish the rational requirements of coherence and consistency from the empirical requirements of applic- ability and adequacy. The requirement of “logical consistency” amounts to “the exemplifi- cation of general logical notions in specific instances, and the principles 1 Michel Weber, Whitehead’s Pancreativism. The Basics. Foreword by Nicholas Rescher, Frankfurt / Paris, ontos verlag, 2006, esp. ch. 1 (pp. 1-64).  Introduction 47 of inference” (PR 3). It obviously refers to Aristotle’s sophistication of the substantialistic logic of common-sense, stabilized so to speak by Boole’s Investigation of the Laws of Thought (1854) in terms of the principle of identity, the principle of contradiction and the excluded middle. In plain language, contradiction amongst categories is to be avoided. The requirement of “coherence” seeks to establish a categoreal de- mocracy in which each category has some genuine weight (independence) and makes sense only in its togetherness with the oth- ers (interdependence). In other words, each category has to bring something specific in the discussion without breaking its semantic tights with other categories. Each has to mirror in its own way the presence of the others. The chief culprit that Whitehead constantly denounces is Descartes and his totally incoherent substance dualism or bi-substantialism. The requirement of “applicability” corresponds to the request for some real interpretative power. There is, in other words, no need to build fully coherent and totally consistent systems if they have no con- crete explanatory power whatsoever. The requirement of “adequacy” asks that “everything of which we are conscious, as enjoyed, perceived, willed, or thought, shall have the character of a particular instance of the general scheme.” (PR 3) It ob- viously constitutes an ideal, a focus imaginarius but it is by no means an innocuous one: radical empiricism shows through it. On the other hand, we need to articulate the four criteria. First, re- spectively at the rational and the empirical level; second, at their necessary conjunctive level. First, Whitehead makes clear that coherence is far more important than consistency: contradictions (unlike paradoxes) are quite easy to fix; lack of coherence, however, definitively cripples a system. “Entia non sunt diminuenda sine necessitate” as Roberto Poli claims. For its part, applicability requires some empirical cash value, while the un- reachable adequacy is the horizon towards which applicability strives. 48 Michel Weber Second, one has to recognize that what matters most is the lure to- wards adequation,1 not the one towards full consistent coherence. As Jean Wahl (1888–1974), among others, saw clearly: the point of British neo-realism is to understand each thing, not all things; lack of consis- tency is preferable to lack of applicability.2 But this still does not bring together the four criteria. In Whitheadian parlance, the unity (or the fouring) of the four is necessity. In a sort of Kantian move (equally reminiscent of the Timaeus), we have to under- stand necessity as the seal or categoreal keystone that brings together the two rational and the two empirical criteria. It does so through a peculiar wager on the rationality of the concrete and on human beings’ capacity to reach it. There is most definitely fitness—no matchness—of our cognitive tools to reality, from the biological and the cultural stand- points alike. This animal faith of sorts furthermore binds everyone together as a human community dwelling in a welcoming cosmos. There are two levels in our claim: factual and existential. First, the fitness of our categories is the result of a threefold process of atunement: phylo-genetic (Spencer: the categories that are a priori for the individual are a posteriori for the species), onto-genetic (Piaget: cognitive categories are developed through sensorimotor and preoper- ational stages) and koino-genetic (Bateson: the convergence of individual consciousness is achieved through learning). Second, each and everyone of us is invited to consciously subscribe to this genetic necessity. This constitutes the philosophical commitment par excellence, but it is by no means restricted to the philosopher, pro- 1 Whitehead does not speak of greater adequacy, only of adequation— hence the focus imaginarius effect involved in his use of the cri- terion. 2 “L’Anglais veut comprendre chaque chose et non toutes choses; il préfère la contradiction dans l’ensemble de la théorie à la mécon- naissance d’un caractère de fait particulier.” (Jean Wahl, Les Philosophies pluralistes d'Angleterre et d'Amérique [Thèse princi- pale], Paris, Librairie Félix Alcan, 1920, p. 87.) See for instance what Whitehead says of religion and dogma in Religion in the Making (1926), chapter II.  Introduction 49 fessional or otherwise. To summarize: the simple singlefoldness of the four is to be found at the level of the existential commitment of the individual who ratifies through his actions the togetherness of the many and thereby goes beyond it. In ancient parlance (that is not necessarily dualistic): we have to fully acknowledge both our terrestrial roots and our celestial destiny. Now there is a very simple concept to name this community in the act: common sense or sensus communis, in which theory and practice, the rational and the empirical, necessarily converge. Granted, we need a refined version of common sense in order to avoid the negative con- notations of the term. Arendt has provided interesting insights here around the notions of intersubjectivity and interobjectivity,1 so did Husserl with his concept of “Urdoxa”2 and Merleau-Ponty with the “perceptive faith”3 that characterizes our belonging to the world: not only are we sure that what we perceive is real, but a momentary sus- pension of perception does not nullify that certainty. A more recent similar attempt actually took place in Whiteheadian studies with Grif- fin’s hard-core common-sense notions,4 that qualify the universal and primordial beliefs that human beings do not question in practice: their fundamental freedom, the causal efficacy of their actions, the existence of a real world, of values and of a temporal drift. What is fundamentally 1 “A three-fold commonness” (Hannah Arendt, The Life of the Mind. One-volume edition, San Diego, New York, London, Harcourt Brace Jovanovich, 1978, p. 50). 2 The Urdoxastic theme is present throughout Husserl’s thinking, from the published work to the Nachlaß: in §104 of the first volume of the Ideen (1913), in his “pre-Copernician” essay (“Die Urarche Erde be- wegt sich nicht” [1934], in Philosophical Essays in Memory of E. Husserl, New York, Greenwood Press, 1988, pp. 307-325), and in the Introduction of Erfahrung und Urteil (1939/1954). 3 Maurice Merleau-Ponty, Le Visible et l'Invisible. Suivi de Notes de tra- vail. Texte établi par Claude Lefort, accompagné d'un avertissement et d'une postface, Paris, Éditions Gallimard, Bibliothèque des Idées, 1964, pp. 17 sq. 4 David Ray Griffin and Huston Smith, Primordial Truth and Postmodern Theology, Albany, New York, State University of New York Press, 1989, esp. pp. 90-91. 50 Michel Weber (necessarily) reasonable is what does not endanger the Urdoxastic vi- tal—carnal—link we maintain with the perceived world. In sum, the concept of necessity that Whitehead activates in the first Part of Process and Reality embodies the fundamental conjunction of the theoretical and the practical sides of life. 3.2. Developmental Typology What can we learn from this typology to provide an answer to the de- bated question—the future status and applicability of process modes of thought? To operationalize the interpretational grid we have just skimmed through, it seems advisable to introduce two further distinc- tions: between insiders and outsiders of a discipline—in our case, between Whiteheadians and non-Whiteheadians—and between convic- tion and persuasion. The former names the straightforward difference existing between Whiteheadian scholars and “specialists” who are nei- ther familiar with the “philosophy of organism” nor likely to get acquainted with it unless some good reason is provided; the latter is the by-product of centuries of rhetorical meditations. To convince someone of something, the speaker needs to talk to the intelligence of his/her audience; to persuade, she needs to mobilize their will. To be convinced is not to be persuaded: I can know for sure that smoking tobacco is lethal in the (more or less) long term but as long as I don’t act accordingly, this knowledge is useless. To be per- suaded is not to be convinced either: I can refrain from smoking for reasons totally foreign to the scientific ones usually broadcasted (say to keep my soul clean and prevent unfortunate metempsychosis) or even for no reason whatsoever—simply because such decision has been spontaneously taken and that it worked so to speak ex opere operato (remember Austin and James’ will to believe). What does it say about the stakes of rationality? First, the bi-directionality of this argument is appropriate only if the idea of a universal reason is obliterated by a healthy relativism. There are no “right” reasons to stop smoking; everyone can have a different one, that can be convincing and perhaps even persuading to others. Of course, science is not a fairy tale and its  Introduction 51 claim to objectivity is well established by internal perfection and exter- nal confirmation as Einstein would say, but science does not address the core of our experience. This brings us to the second point: the fundamental rational—not experiential—opacity of the common world. Now that we are equipped with these complementary concepts, we can rephrase the question of this special issue: under what categoreal conditions will scholars be not only convinced but also persuaded of the virtues (rather than the vices) of Whiteheadian process thought? In order to keep our discussion tight, we will add an additional filter in- spired by the current way debates are lead (or prevented) in the Academia. That filter is not dogmatic but heuristic; it constitutes less a bold claim than an obvious simplification that allows to obtain promptly a provisional synthesis. Let us start with our hypothetical universal fact (or filter): specialists (almost) never seriously talk to scholars who do not happen to share the very same expertise—unless these fall under the category of “stu- dents” and in that case they are equally likely to talk at them. Exceptions put aside (and they are all the more remarkable), debates are usually taking place among the happy few who share the same concern about one field of expertise and do not really need to expose endlessly their presuppositions and the meaning and significance of their concepts. In short: never is the expert knowledge put at risk by a truly open discussion. Besides the equally obvious power games that take place within a given domain, what strikes the internal observer is the emphasis on rational conviction. Rational points here at the nature of the arguments that tend to focus on issues of coherence and consistency. Empirical conviction would animate another theatre, as we will shortly see. Specialists have that faculty of enjoying only the philosophical writ- ings of their elected single philosopher. Philosophy is clearly a very personal matter and one can see the affection that can bind, through the ages, the reader and the author. But hagiography should be avoided at all costs, for the simple reason that it is the sure sign of the immi- nence of inert ideas. Within the Whiteheadian field itself, the accent 52 Michel Weber tends to fall more on bare conceptual matters than on empirical ones. Hence a first conclusion: what the specialist can achieve among his/her peers is to see his/her interpretation recognized as consistent and/or coherent. But such consensual discussions have absolutely no impact whatsoever on the outsiders: in the very same way that Whiteheadians are not likely to entertain the reconstruction of the late Heidegger’s puzzle with his own categories (“Raum”, “Eingeräumtes”, “Freigege- benes”, “Grenze”, Wesen”, “Begriff”…), Heideggerians have no interest, say, in the togetherness of “Many”, “One” and “Creativity”. Nobody denies that the concept “horismos,” that is of horizon or boun- dary, can be activated in both cases, but such cross-elucidatory path seems a waste of time and, if not, it would be foolhardy to proceed without first devoting some serious thoughts to the conditions of possi- bility of such a dialogue (something, by the way, that is precisely allowed by the intricated levels of meaning that are systematized in Whitehead’s definition of speculative philosophy). To further exemplify: this rationally convincing type of work has been done by the journal Process Studies that has no doubt firmly established excellent standards in Whitheadian scholarship and thereby created a “process com- munity” but, like all other specialised journals, it has done so by securing the field. If we now turn our glance on the empirical side of Whitehead’s defini- tion, the converse situation is expected. On the one hand, internal debates are often too much tangled to conceptual issues to really worry about their pragmatic cash-value, that are taken for granted. On the other hand, external debates are the place where an advantage in ap- plicability can make all the difference. In the case of Whiteheadian scholarship, quantum physicists constitute perhaps the best example of such an interest expressed from the standpoint of the applicability of Whitehead’s categories (most recently: Shimony, Stapp, Malin, Hättich, Epperson…). In other words, whereas insiders are expected to be con- vinced mainly by rational fiddlings, outsiders are likely to be convinced only by the manifestation of a significant differential in applicability. To repeat: we do not deny that this heuristic sketch is in part an imagina-  Introduction 53 tive simplification—what matters are the pragmatic consequences that could be drawn from it. So far we have two general cases: insiders and outsiders are con- vinced by different reasons—but when are they persuaded? Quenching one’s intelligence is one thing, acting accordingly is another. What makes the difference between conviction and persuasion? When does the philosophical reflection become necessitating? (When does it neces- sarily impact behaviour?) Could it be simply when there is a total correlation between the life of the philosopher and his/her rational and empirical concerns? Here is for instance what Flanagan claims: Simply put, the attraction of James the philosopher is that he is to me the best example I know of a person doing philosophy; there is no hiding the person behind the work, no way of discussing the work without the person, no way to make believe that there is a way to do philosophy that is not personal.1 The heuristic hypothesis inspired by the reading of Whitehead’s defini- tion of speculative philosophy is thus the following: persuasion strikes when rational and empirical conviction merge, an event that takes place under the spell so to speak of an individual who is precisely em- bodying that synthesis. To conclude our exercise of applied typology: we argue that insiders and outsiders are likely to be convinced of the relevance of some form of Whiteheadian process thought for different reasons. But this still does not say much about their persuasion. Living philosophy needs to be a lived philosophy. Whiteheadians will not only convince their fel- lows philosophers and scientists but persuade them of the value of their categories when they will be themselves living philosophical—spiritual if you like—examples. Socrates would have talked about the call of authenticity, Whitehead provides two concepts to specify this in a per- haps more pedestrian manner: duty and reverence. 1 Owen Flanagan, “Consciousness as a Pragmatist Views It”, in Ruth Anna Putnam, ed. The Cambridge Companion to William James, Cambridge, Cambridge University Press, 1997, p. 47. 54 Michel Weber 3.3. Duty and Reverence in the Light of the Creative Advance According to Whitehead, Duty arises from our potential control over the course of events. Where attainable knowledge could have changed the issue, ignorance has the guilt of vice. And the founda- tion of reverence is this perception, that the present holds within itself the complete sum of existence, backwards and forwards, that whole amplitude of time, which is eternity.1 This claim, that occurs in the specific context of a philosophy of educa- tion lecture, has a direct relevance to our discussion. First because it points at the “religious” dimension of education that mirrors the spiri- tual dimension of existence. Second, because it is easy to see at work in these lines the conditions of possibility of the “creative advance” itself. To argue that the core concept of the late Whitehead is the “cre- ative advance of nature” is an inspiring move that discloses three fundamental characteristics of all processes—creativity, efficacy and vision. All actualities (according to their grade) are creative in so far as they embody new contrasts and intensities in a new extensive region (in the technical sense of Process and Reality’s Part IV). By definition, the ex- tensive region occupied by the new actuality was never occupied by any actuality and will never be occupied again by some other actuality; furthermore, the exact same contrasts were not possible before and will not be possible after the given concrescence; the intensity of its experience, in so far as it is eminently private, is sepulchral, incompar- able. Actualities are efficacious through their structural (objective and super- jective) world-loyalty. Every actuality springs from the efficacy of its past (or prehended “actual world”) and, in its turn, occasions a certain 1 Alfred North Whitehead, The Aims of Education and Other Essays, New York and London, The MacMillan Company and Williams and Norgate, 1929. Reprint: New York, The Free Press, 1967, p. 17.  Introduction 55 type of future. The comparison of embodied intensities is only possible in this structural context, i.e., ex post. Actualities are visionary through the instantiation of a trend towards higher intensities of experience. The sole interplay of creativity and efficacy does not guarantee any creative advance at all, only the ruth- lessness of existence. Creativity is indeed totally wild while efficacy imposes a blind necessity upon the creative outbursts. It has been often remarked that Whitehead was a Victorian gentleman whose supreme optimism had been directly inspired by the techno-scientific utopia of his peers (cf. Thomas Henry Huxley), which is itself inseparable from his Zeitgeist, made of nineteenth Century Romanticism, of Darwinian evolutionism, and of a blind faith in the accelerating industrial revolu- tion and in the civilizing importance of British colonialism. From the perspective of human beings, creativity is thus the crux of the creative advance, but it is by no means the entire story: efficacy involves duty and vision involves reverence. Ignoring duty and rever- ence would be equivalent to act as if we were stuck at Piaget’s preoperational stage (roughly ages 2-7, when motor skills are coordi- nated but without any significant mental actions on objects)—or even perhaps at the sensorimotor stage (roughly ages 0-2). The thirst for creativity would be unquenchable and its likely outcome probably full of sound and fury. In sum, creativity and philosophical commitment cannot be parted from one another. The strong processual context advocated by White- head asks us to become worthy of the creative advance, which involves preciously cultivating duty and reverence. The individual who achieves this worthiness will be persuasive. The future of Whiteheadian scholar- ship depends indeed upon creative individuals who are able to take upon themselves the living ideal of philosophy and to be thus a vibrant example for their community and beyond. But isolated individuals, whatever their creativity, cannot achieve much without institutional support (and when they do, this gives only a meagre idea of what they could have done with proper support). Last but not least, without vi- sion, the creative individual cannot really benefit from whatever 56 Michel Weber structural support at his disposal, his/her output will only be the result of chance backed by necessity. In this year 2010, a Whiteheadian scholarly tri-une archetype comes to mind: John Cobb, Claremont’s Center for Process Studies and a cer- tain Christian vision for the common good. In Whitehead’s words: Morality of outlook is inseparably conjoined with gener- ality of outlook. The antithesis between the general good and the individual interest can be abolished only when the individual is such that its interest is the general good, thus exemplifying the loss of the minor intensities in order to find them again with finer composition in a wider sweep of interest.1 Right wing philosophy, that roots itself in a standpoint seeking to pro- mote only one’s own interest, which means, directly and indirectly, to foster the alienation of the hoi polloi by the aristoi, of the multitude by half percent of the population, is a tragic oxymoron—full stop. Interest- ingly it translates either as a total political immaturity or as political senility. Developmentally speaking, it is indeed well-known that only adults can escape the egoism ingrained in every human being —and the point is that this road towards civilization is paved by reason, not by feeling. Now, neither creativity nor vision can be taught. Vision can be shared or suggested by interplay of scholarship and commitment—not learned. Creativity is a universal gift that has to be activated by the individual who decidedly takes the risk of adventure. When Whitehead speaks of adventure he obviously thinks more about a successful Vic- torian exploration than about the tragedy of the elusive authenticity of existence and it is thus advisable to temper his fundamental optimism with the help of William James, who has indeed shown unambiguously that the philosophical quest is intrinsically risky (remember Plato's “beautiful risk” ). Efficacy is the easiest bit in so far as it involves only (!) material and intellectual resources that can be pragmatically made use of. 1 Process and Reality, p. 15.  Introduction 57 Who else than a prophetic process poet could provide the right ban- ner for our speculations? In Blake’s œuvre, Urizen refers both to the horizon of our civilization and to your reason as it shapes our common destiny. When reason is bifurcative, reductive, when it most desires “joy with- out pain” and a “solid without fluctuation” (Urizen, Chapter 2), it is a closed horizon that is in the making and a doomed future that torments if not threatens all forms of life. Persuasion is in vain. When reason is holistic, the open horizon of the creative advance can again animate our very existences and, through duty and reverence, announce liber- ation. This must be the reason why education— the art of the utilisation of knowledge—has to be, in Whitehead’s lexicon, religious. In James’ lexicon, it is a matter of frist-hand experience. According to process philosophers, “[t]he problem with the man is less what act he shall now choose to do, than what being he shall now resolve to become.”1 The same holds for schools of thought. 1 William James, Principles of Psychology [1890]. Authorized Edition in two volumes. Volume Two, New York / London, Henry Holt & Co. / The MacMillan Company, 1890, Vol. I, p. 288, debating Schopen- hauer.  II Reading Whitehead Randall E. Auxier It has often been remarked that Whitehead is difficult to read, and the- re can be little doubt that the challenge of his language is partly responsible for limiting the influence of his philosophy. The difficulty, however, is not just mastering a new vocabulary. In some ways the problems with reading have much to do with the unfamiliarity of the individual thoughts and relations among ideas Whitehead describes, and this situation is not so much linguistic as intellectual. The ideas themselves are not easy to think. But to this we must add that it is not always easy to grasp the structure of Whitehead’s exposition because it operates simultaneously at several levels of abstraction (or generality), and Whitehead is in the habit of moving from one level to another with little warning he has done so. Whitehead does define his vocabulary carefully and he does describe the various levels of generality, and he is conscientious about laying out the scope, limits and aims of every in- quiry. But he tends to over-estimate his readers. The effort to understand Whitehead is further complicated by the or- ganic character of his thought. Each part of his philosophy, every level of generality, every term, and every goal, is immanent in and achieved through all of the others. To understand any passage in one of White- head’s books requires an understanding of the rest of the book. Whitehead is not one to waste words, and there is an amazing econ- omy to his language, so unpacking the full meaning of even a single sentence, in light of the work that sentence does in the book, can re- quire a long narrative. Organicity in a philosophy is something that is familiar to readers of Hegel, Bradley, Bergson, Royce, Heidegger, and numerous others, but the problem is especially pronounced in White- 60 Randall E. Auxier head’s most important works, since the order of exposition is often very different from the order in which the ideas would be traced if the exposition were linear. In addition to these problems, we may add that there is also a great difficulty in understanding how one work by Whitehead, whether an essay or a book, relates to or bears upon others in the full corpus. Here we have to confront issues of the development of Whitehead’s thought, but also the unity of it. Many incompatible interpretive theses have been defended by various scholars over the decades, but the most popular and influential theses usually involve the idea that Whitehead’s thought culminates in his 1929 work Process and Reality, which is by any standard the heart of Whitehead’s philosophy, and that all other works are to be measured by the standards set in that work. I do not believe this prevailing view is either correct or helpful in learning to read Whitehead, so I will not assume it in what follows. 1. Whitehead’s Lexicon To begin the daunting task of “reading Whitehead,” it is a good idea to start with a discussion of terminology and how it is deployed in service of systematic inquiry. Whitehead organized his inquiries in the way mathematicians do, defining terms flexibly and generally, and redefin- ing them when he changed from one inquiry to another. Thus, for example, what he calls “eternal objects” in Process and Reality has a close relation to what he calls by the same name in Science and the Modern World, and both are close to what he calls “ideal forms” in Religion in the Making, but there is no reason to assume an identity of meaning for technical terms across differing books. Indeed, the mean- ing of technical terminology develops and deepens more within the context of a single inquiry than across books, so that there is no reason to assume that a technical term, such as “ideal form,” means exactly the same thing from one occurrence to the next within even the same book, let alone across books. For example, in Religion in the Making, the term “ideal forms” is used more or less interchangeably with the  Reading Whitehead 61 terms “ideal entities,” and “abstract forms” and all are closely related to the term “ideal world.”1 Whitehead says that “the fate of a word has to the historian the value of a document.”2 To be a reader of Whitehead is to be a historian of a sort, and the fate of each word is certainly a document in the relevant sense. But Whitehead’s writing style tempts one to treat individual occurrences of technical terms as though they might serve as fixed definitions. He has a habit of saying things like “an actual entity is the outcome of a creative synthesis, individual and passing.”3 But else- where he may say something like “to be an actual entity is to have a self-interest,”4 which seems to have no clear relation to what has been said before, but also seems to have definitional force. As a matter of writing style, Whitehead makes hundreds of statements like these in his shorter works, and thousands in the longer works. Even if it were clear what force a definition has in Whitehead’s thought (and that could be a long discussion), it would never be clear when he intends a given statement to have definitional force. It is bet- ter to think of the occurrence of terminology in Whitehead in hermeneutic terms, to see each occurrence of a term as a promissory note of further refinement, in terminology and in total context, over the course of a work. There is, however, no such promise of refinement when we move from one work to another. Whitehead’s philosophy does develop and fill out. His numerous footnotes in later works to earlier works suggest that he thought of the various inquiries in relation 1 See the edition of Whitehead’s Religion in the Making that contains my comprehensive glossary (New York: Fordham University Press, 1996), which is edited and introduced by Jude Jones. I am drawing this example from p. 182. The glossary exhaustively cross- references and defines all technical terminology and fills pp. 161- 251 of this edition. I created the glossary for the express purpose of teaching Whitehead to people who would be frustrated by his vo- cabulary and by what may seem to be slippage in his use of it. 2 Whitehead, Religion in the Making, p. 128. 3 Ibid., p. 93. 4 Ibid., p. 100. 62 Randall E. Auxier to a total development and effort, but with terminology he makes no such assurances. In the domain of technical terminology, the safest interpretive course is to confine one’s attention to a single work until the full meaning of the term in that context has been appreciated and understood. Only then is a reader in a good position to consider how the differing aims of various books may affect the comparison of ter- minology that may seem similar or even be common to both. For example, the subject matter of Science and the Modern World (1925) is not too far removed from that of Process and Reality (1929) since the latter treats cosmology, which Whitehead understands as a subdivision of scientific thinking, which is the topic of the former. We might expect very similar meanings to be associated with similar or identical terminology, and the expectation is, I think, fulfilled. But the context of usage does make a difference, the aims of the two inquiries are different, and comparisons in meaning should always resist the urge to assume premature identities of terminology. Thus, not only should we refrain from asserting simple definitions within a single work, we should be even more reluctant to assume identical definitions from one work to another. To use the meaning given to a term in one work as the standard to which occurrences of similar (or identical) terms must be measured (as is lamentably common among scholars of process thought) denies to each inquiry the relative independence Whi- tehead claims for each work and over-emphasizes the continuities among them in ways that are sure to distort one’s reading and under- standing of Whitehead. Whitehead’s philosophy of language actually requires such caution as is advised here. Not only is error the ground of meaning for Whitehead, but he continually complains about the poverty and inadequacy of lan- guage. It is best to take the development of terms in each of Whitehead’s works as open-ended but increasingly adequate meta- phors that point to some fundamental relation —a relation that will not come fully to language. A definition for Whitehead is not the demon- stration of an essence from first principles, or from the four causes. He does not accept the idea that predication (whether traditional or Kant- ian) is our best route to capturing the meaning of an experience.  Reading Whitehead 63 The best place to begin one’s study of Whitehead’s usage is to read Religion and the Making in conjunction with Science and the Modern World. Because the two works were written in the same year, one can largely ignore the question of whether a time lapse has affected White- head’s thinking. Whitehead says that these two books are the same train of thought in different applications, so variations in terminology are just as informative as similarities. To master Whitehead’s usage, then, means to grasp first the fate of terms within a single work, and to begin to grasp what is involved in comparing terminology from across works, starting with the easiest. Another option is to compare The Con- cept of Nature to Inquiry into the Principles of Natural Knowledge, which treat similar questions at different levels of abstraction, but these are more demanding works and for that reason perhaps less than ideal for mastering vocabulary. In addition to what is said here, it is sometimes but not always illumi- nating to trace the origins of the technical terms Whitehead chose for his system beyond his own works. For example, the term “ingression,” which Whitehead uses for the way eternal objects enter into concres- cence, may seem like a neologism, but it isn’t at all. It goes back to Middle English and has a long-standing legal meaning, and has been adapted to mathematical and economic uses over the centuries. Simi- larly, sometimes the odd word “prehension” is attributed to Whitehead, but its use dates back at least to 1828 and has also a legal meaning. Whitehead, in spite of appearances, is wary of neologisms, but not wary of making full use of the English language and adapting existing terms to new shades of meaning. As you might expect, however, these adaptations are dynamic and developmental. The introduction of a new term, never undertaken lightly by Whitehead, is just the beginning of a process of getting it to do the work he has in mind for it. The cluster of essential terms becomes a mutually defining organic whole. That whole is firmly in Whitehead’s mind before he writes a book, and the order of exposition in the book is independent of the process by which his thinking proceeded in developing the web of meanings. Thus, fully grasping one term requires fully grasping all of the terms, and not con- 64 Randall E. Auxier fusing the order of their exposition in a work with their mutual relations of meaning. For this reason, it can be difficult to know where to begin. It will be clear that among the strategies I recommend, a good one is listing occurrences of key terms and compiling near verbatim sum- maries of the meanings Whitehead attributes to them, which is what I did in the glossary to Religion in the Making, while Sherburne has done something similar for Process and Reality. This is obviously a labor- intensive process. One might use my glossary as a substitute for doing that work, and to a lesser degree, Sherburne’s A Key to Process and Reality may also be consulted, although its scope is limited and it does not try to preserve the order of usage in the book —thus the develop- ment of terms is often lost. I certainly learned a lot in making my own glossaries. However, even doing this kind of work for yourself will not necessarily take you to an adequate understanding of what you are reading. Some other principles have to be understood. 2. Whitehead’s Structure of Inquiry I will now make a suggestion as to how we should understand the structural organization of Whitehead’s inquiries in various works, and how, for him, “method” is subordinate to “theory,” or working hypoth- eses, therein. The first thing to be aware of is that Whitehead is not attempting phenomenology in any of his inquiries. The description of experience that (in effect) denies both genuine discontinuity and continuity to the perceptual flux, substituting for that flux some sort of Fürsichsein or intentional condition (by some epoche or reduction), so as to discover discreteness and continuities in acts of consciousness (and structures and principles) is not Whitehead’s aim. He knows very well its import- ance, but it is not his task. If Whitehead were to have a phenomenology, it would, I think, look very much like the one Ernst Cassirer created in The Philosophy of Symbolic Forms (1923–1929), since the relation of culture and nature were Whitehead’s main pre-  Reading Whitehead 65 occupations, rather than consciousness and psychology. The complementarity of Whitehead and Cassirer is instructive and worth examining because Cassirer’s project brings to Whitehead the kind of phenomenology his thought requires. Wilbur Urban, who contributed essays to both of the important Li- brary of Living Philosophers volumes on Whitehead and Cassirer,1 identifies the central issue in attempting to bring their ideas together as follows: If the ideal form and immanental law of all knowledge is, indeed, to be found in the mathematical-physical sciences, then it would seem the symbolism of metaphysics must also be a symbolism of relations and that a philosophy of events, such as that of Whitehead for instance, would ne- cessarily be the resultant metaphysics. On the other hand, if it is true, as we are told by Cassirer, that science as symbolic form has no exclusive value, but is only one way of constructing reality, and has value only from the stand- point of science, then it would appear that a metaphysics, to be adequate, must be a metaphysics of art and religion also and must have a language and symbolic form which includes these forms also —in which case it could no longer be a symbolism of relations merely, but must be a symbolism of things also.2 Here Urban expresses a point of view quite common not only among critics of both Whitehead and Cassirer, but even among their most sympathetic interpreters. The effort to treat science as both an inde- pendent and culturally embedded form of knowing is at best a delicate task. The main failure of understanding in Urban’s comment is that he does not grasp “relation” as a concrete metaphysical hypothesis, but sees it only in its logical or mathematical sense, seeming to assume that method is prior to theory. He has not understood that for Cassirer 1 See Paul Arthur Schilpp, ed., The Philosophyof Alfred North Whitehead (LaSalle, IL: Open Court Press, 1951 [1941]); and The Philosophy of Ernst Cassirer (LaSalle, IL: Open Court Press, 1958 [1949]). 2 Wilbur Urban, “Cassirer’s Philosophy of Language,” in The Philosophy of Ernst Cassirer, 437-438. It is interesting that Urban was also re- ferred to by Langer as setting her problem up in the preface to the first edition of Philosophy in a New Key. 66 Randall E. Auxier and Whitehead, there are no “things,” in science, religion, art, or any other symbolic domain, until the “things” are constituted as the highly mediated outcome of a symbolization process. Nor has Urban appreci- ated that art, religion, etc., are modes of symbolization, ways of relating to and having a “world.” They invite separate inquiries with methods and ontologies adapted to their variations. Urban has rightly intuited that a metaphysics of events like White- head’s is appropriate to the type of philosophizing Cassirer is doing, but he has not considered that there are “events” in more than the scien- tific sense of the term. Understanding Whitehead involves the recognition that even if, for instance, “artistic events” and “scientific events” are both “events,” the price one pays for seeing them in such an abstract way as to unify them under a single term is that one forfeits most of what makes them interesting, valuable and even knowable. To know something abstractly is not to know it very intimately. Certainly the factors that point to the fact about an event seen in the light of art and the factors that point to the “same” event as a fact of science are, in many ways, positively correlated, but there is no good empirical reason to assume the ontological identity of the facts thus picked out by those factors. Yet, Urban rightly recognizes that the tendency of Cassirer, in keeping with Whitehead, to endow science with the highest authority in “know- ledge” is puzzling to many in light of their similar claim that science is an embedded and thoroughly mediated form of culture. Whitehead and Cassirer are indeed both philosophers of science in the highest sense. Urban, like so many other 20th century realists, is assuming that sci- ence, done rightly (i.e., according to its supposed “method”), has a privileged ontological path to the way things are, independent of the knowing mind. But the question of mind-independence is a holdover from substance metaphysics, with its assumption that there is some necessary relation between “knowing” and “being” (and that this rela- tion is secured in mathematical or logical relations). Where one assumes only possible relations between reality and knowing, and places necessity strictly within the internal operations of knowing, re- ality becomes a contingent process. On this point Cassirer and  Reading Whitehead 67 Whitehead agree, and in no way does this restriction reduce the auth- ority of science. The move to treating possibility as the fundamental modal category in metaphysics simply allows us to situate scientific knowing historically and empirically and account for the growth and alterations in our scientific claims. But philosophy deals not with nature or religion or art directly, it deals with the structures of their possibilities foremost. As Whitehead says: “Philosophy is the ascent to the generalities with the view to under- standing their possibilities of combination. The discovery of new generalities thus adds to the fruitfulness of those already known. It lifts into view new possibilities of combination.”1 Its aim is philosophical knowledge. It is worthwhile at this point to give special note to some- thing Whitehead often says near the beginning of his inquiries. Whitehead complains often about how little philosophy can really ac- complish, blaming this usually upon “weakness of insight and deficiencies of language.” (PR 4) As a result our initial descriptions re- main “metaphors mutely appealing for an imaginative leap.” (ibid.) The difficulty, he continues “has its seat in the empirical side of philoso- phy”: Our datum is the actual world, including ourselves; and this actual world spreads itself for observation in the guise of the topic of our immediate experience. The elucidation of immediate experience is the sole justification for any thought [note, not just philosophic thought]; and the start- ing-point for thought is the analytic observation of components of this experience. But we are not conscious of any clear-cut complete analysis of immediate experi- ence, in terms of the various details which comprise its definiteness. (PR 4) This is the cost of a radical kind of empiricism.2 With this issue under- stood, it is nevertheless true that Cassirer and Whitehead undertake 1 Whitehead, AI, 235. 2 For a fuller account of what is meant by “radical empiricism” here and Whitehead’s relationship to it, see my “Whitehead’s Radical Empiricism: Mementoes of a Timequake,” in Applied Process Thought II: Following a Trail Ablaze, ed. Roger Mark Dibben and Rebecca Newton (Frankfurt am Main: Ontos Verlag, 2009), 75-100. 68 Randall E. Auxier very different projects, phenomenological and metaphysical respec- tively, from the same basic convictions about process and reality. I see no fundamental disagreement between the two, but I believe that few interpreters rightly understand their full complemetarity. Interpreters of Whitehead have commonly confused the issue of the development of his ideas, the genesis of them in his intellectual biography, with the meaning and purpose of his individual works. It is common for them (Lewis Ford is a good example) to think of each book as presaging some further development of the whole philosophy of organism, cul- minating, for most, in Process and Reality, with the two major books he wrote thereafter drawing out consequences. There is great value in studying Whitehead’s development, but it has led most readers to over- look the common pattern in each of his books, and very often they have misunderstood his method (and how it is dictated by a different working hypothesis in each book) along with his way of structuring an inquiry. The structure of the inquiry is essentially the same in each book, but the methods vary with the hypotheses under consideration. Whitehead is always careful in his introductions to supply a clear indi- cation of where his present inquiry fits in the general effort of thought (which is his philosophy itself). He carefully qualifies the project at hand and suggests its limits. The proper “criticism of a theory,” or “working hypothesis,” for Whitehead, “consists in noting its scope of useful ap- plication and its failure beyond that scope.”1 Whitehead scholars have not been careful about this point, giving inadequate regard to his own statements of scope and purpose. But in truth, each book is an individ- ual inquiry into some important domain of experience. Each book proceeds along the same basic line: he will describe the phenomena under investigation to provide a version of them, how they may be seen (not how they must be seen), and then he subjects that descrip- tion to a systematic analysis. In no instance does he claim that the initial description of the phenomena (what he calls their “genetic ac- count” in PR) is the final or the only way of describing these phenomena. In every case he notes that their analytically detailed and 1 Whitehead, AI, 221.  Reading Whitehead 69 systematic characterization (what he calls the “co-ordinate account” in PR) is dependent upon the genetic description, but the co-ordination of the phenomena sets the scope of the inquiry and their genetic descrip- tion is limited by that scope. Co-ordination of the phenomena is closer to the way they are experienced than is their genetic specification. In adopting this structure Whitehead follows standard mathematical methods. One must specify the entities and rules before proceeding to their systematic interrelations. There is a great deal of freedom in specifying the phenomena or entities genetically, but the test of whether it has been done well is whether interesting systematic rela- tions, “new generalities” and “possibilities of combination” do come to light in the co-ordinate phase of the inquiry. And the whole inquiry, both genetic and co-ordinate, is measured against the ways in which it illuminates experience. In answer to the question “why should we ac- cept this genetic account?” Whitehead holds that its warrant looks back to experience, first, and attempts as accurately as possible to carve out the phenomena under discussion in ways that accord with our experi- ence. Adjustments in this genetic account are inevitable in light of our further investigation of the phenomena. In spite of that, we are justified in specifying the phenomena to the best of our ability for the purposes of a more thorough speculative understanding of their interrelations. The adjustments along the way of terminology, as discussed above, are justified by the way that the initial specification of phenomena is too abstract, too stipulative, and needs concretization. Thus, the genetic phase of an inquiry is an initial spatialization of the phenomena, under descriptive principles determined by the purpose of the investigation at hand, more specifically, the working hypothesis or “theory,” the common character of which is to sequence and specify those phenomena, i.e., to limit what we mean in referring to them in that context so that we can discuss them systematically. The sequen- cing (and hence spatializing) does not have to be historical or chronological, but it can be, as in Religion in the Making and Adven- tures of Ideas. In every case, however, the aim is to get the phenomena to “stand still,” to provide a conceptualization which controls for their 70 Randall E. Auxier ephemeral and changing character so as to provide us with something we can trust from one thought to the next. With the initial genetic description in place, and the flux controlled, we can move to a co-ordinate analysis. This is a second order spatiali- zation that allows us to examine and bring to light systematic features that were immanent in the initial genetic specification of the phenom- ena. The exhibition of these relations presumably enables us to see how our own activity of characterizing phenomena genetically will ne- cessitate certain conclusions about their relations and exclude other conclusions. To alter the necessitated results of a co-ordinate account, one must back up and alter the genetic account, and in so doing attend again to the ways in which experience presents those phenomena in together that we had singled out and specified for an initial genetic description. Experience comes together, genetic description specifies, and co-ordinate description restores some portion of the togetherness we lost in specifying, but according to some purpose. The effect of the process is to produce a co-ordinated description that approximates our original experience but is adapted to the aims for which the inquiry was undertaken. The co-ordinate description should exhibit just those char- acters in experience which are relevant to our defined purposes which produced the inquiry. The entire undertaking is thoroughly hypothetical. No conclusion about reality in itself is forced upon us by any result in the genetic or co-ordinate accounts, because the option always remains in White- head’s method of altering the purpose or scope of our inquiry, or of describing the phenomena genetically using different principles of spe- cification. No ontological knowledge is claimed for any result, by which I mean, no knowledge of any necessary relation obtaining between the way things are in themselves, our logic, and our knowledge. It is taken for granted that the relationship between experiencing and philosophi- cal understanding is thoroughly contingent, yet there are still pressing reasons to attempt to gain philosophical knowledge, even if that knowledge is only descriptive. Philosophical knowledge of a subject allows one to recognize important possibilities within the adventure of living which will be overlooked without it, to the great diminishment of  Reading Whitehead 71 of life. Human progress, to the extent that it is possible, has always involved the sort of recognition of possible connections that philosophy brings. Thus, Whitehead’s books are individual inquiries into well- circumscribed aspects of experience, submitted first to a genetic de- scription and then to a co-ordinate analysis, the results of which are limited by the way in which the initial inquiry and its purposes were defined. When Whitehead confronts the phenomena of religious ex- perience in Religion in the Making, for example, he is not immediately interested in their implications for modern cosmology. He does not describe these phenomena in RM for the purpose of seeing their rela- tion to cosmology, or science of any other kind; rather, he describes them for the purposes stated: “to give a concise analysis of the various factors in human nature which go to form a religion, to exhibit the in- evitable transformation of religion with the transformation of knowledge, and more especially to direct attention to the foundation of religion on our apprehension of those permanent elements of reason of which there is a stable order in the world, permanent elements apart from which there could be no changing world.” (RM, Preface) When similar concepts come up, describing similar phenomena, in Process and Reality, they have been described for a quite different purpose, that of investigating “a phase of philosophic thought which began with Des- cartes and ended with Hume.” (PR, xi). In reading the interpretive literature, one gets the impression that Whitehead’s followers simply do not believe him when he states explic- itly what he is doing and why, in spite of the fact that he goes on to explain in detail what limits he places upon each inquiry. The inquiry in PR is about the way philosophers thought between Descartes and Hu- me, a certain turn of thinking, novel in human history, in which the algebraic and geometrical modes of thought came together. PR makes no attempt at a full assessment of philosophic thought from Kant for- ward or prior to Descartes. Whitehead thinks the modern philosophers had some things right that became obscured after Kant. He wants to draw out what they had right. The method (genetic and co-ordinate analysis) is post-Kantian, but not the subject of the inquiry, i.e., Modern 72 Randall E. Auxier cosmology. Thus, Whitehead’s major work attempts to come to terms with the fundamental insights of Modern philosophy, which is not un- like Cassirer’s initial project. Another clear example of the ordering of “genetic” and “co-ordinate” analysis is hard to miss in Adventures of Ideas. Part I of that book speci- fies genetically, in the mode of the history of ideas, of “the influence exerted by the Platonic and Christian doctrines of the human soul upon the sociological development of the European races.” Part II specifies genetically “the influence of scientific ideas upon European culture.”1 The transition to the co-oridinate account is in Part II, where Whitehead breaks with his earlier narrative style, numbers the paragraphs into a categoreal scheme of the essential ideas that have been genetically specified, and then proceeds in subsequent chapters to analyze them in co-ordination with one another. The book’s subsequent structure re- quires that we pay close attention. The break between the co-ordinate analysis and the results of it does come when Whitehead moves to Part IV, but he does not there explain it. For whatever reason, he saves the explanation for the beginning of the final chapter, but he is perfectly explicit about what he has done and how. He says: Our discussions have concerned themselves with speciali- zations in History, of seven Platonic generalities, namely, The Ideas, The Physical Elements, The Psyche, The Eros, The Harmony, The Mathematical Relations, The Recepta- cle. The historical references have been selected and grouped with the purpose of illustrating the energizing of specializations of these seven general notions among the peoples of Western Europe, driving them towards their ci- vilization.2 The selection was done in the genetic accounts of Parts I and II, and the grouping was done in the co-ordinate account of Part II. These are sim- ply other names for genetic and co-ordinate analysis. In a way, one can see that these Platonic ideas function similarly in the domain of a phi- losophy of Western civilization as “symbolic forms” function for 1 Whitehead, Adventures of Ideas, 103. See also the “Epilogue” to Part I on p. 100. 2 Ibid., 284.  Reading Whitehead 73 Cassirer’s much broader “philosophy of culture.” Whitehead goes on: “Finally, in this fourth and last Part of the book, those essential quali- ties, whose joint realization in social life constitutes civilization, are being considered. Four such qualities have, so far, been examined: — Truth, Beauty, Adventure, Art.”1 Such structural statements as these are the ones that reveal Whitehead’s method, and they cannot be over- looked. For Whitehead, “Truth,” for example, does not mean the same thing from one inquiry to another, for scientific truth and historical truth are related but separate ideas, and they require different genetic phenomena and co-ordinate analysis to show their respective mean- ings. To assume, for example that the account of “Truth” in Adventures of Ideas trumps the account in Inquiry into the Principles of Natural Know- ledge, or Science and the Modern World, or Process and Reality is simply to miss what Whitehead does in a book. It is to generalize the results of one inquiry into or out of the results of another in which the phenom- ena have been genetically specified for other and different purposes, and co-ordinately analyzed differently, with different results. It cannot be assumed that later books reveal a development or change in White- head’s basic ideas. Perhaps there is development, but it is not shown to be the case simply because he says different things about, for example, Truth, in later books. What Whitehead says about Truth in Adventures of Ideas is tied intimately to the genetic specification and co-ordinate analysis of truth in that book, and for its purposes. It has to do with the way the idea of truth contributed to the growth of Western civilization, in that book, and not more than that. The results of any inquiry are dependent upon this general way of approaching problems. Results are revisable even within a single inquiry. One can genetically specify dif- ferent phenomena, or the same phenomena in other ways. The co- ordinate analysis is more restricted, because of its answerability to the genetic specifications, but from any genetic specification, infinitely many co-ordinate analyses may be undertaken. 1 Ibid. 74 Randall E. Auxier The criterion by which we adjudge the entire process to have been done either well or poorly is the criterion of experience, for every in- quiry, although one always needs to say what aspects of experience are most relevant to forming such criteria. In general Whitehead does ad- here to “adequacy,” and “logical rigor,” and “exemplification” as functional criteria. These are the criteria made explicit in Process and Reality. All of these criteria are experiential, but in different ways. It would not distort what Whitehead has done in every book to say that: (1) “adequacy” applies most directly to whether the genetic specifica- tion is both in agreement with the phenomena it selects from experience (that these phenomena do occur and are appropriately specified), and whether those phenomena are representative of experi- ence more generally, not simply within the domain of the inquiry at hand; (2) “logical rigor” (or coherence or necessity, which come to the same thing) deals with whether the phenomena, as genetically speci- fied, are analyzed in accordance with logical principles both appropriate to the genetic specification, and without illicit inferences and contradictions and undischarged assumptions when we move from one level of generality to another; (3) “exemplification” (and/or applic- ability) deals principally with whether the outcome of (1) and (2) does indeed illuminate our actual experience as had. There is nothing in this procedure that is in the least out of line with radical empiricism as Wil- liam James defined it. It is simply more worked out than anything James ever managed. To use Whitehead’s results from one inquiry in another context, for instance, from Process and Reality to some other problem than Modern philosophy, requires that we analogize, but in this case we would be obliged to re-describe the phenomena in the genetic mode for philo- sophic thinking since Kant if we wish to use the results, and of course, the results would be correspondingly modified. The analogies from one of Whitehead’s inquiries to another are rich and tempting. And there is much in Whitehead’s earlier works, especially on the developments in science, and several explicit discussions of Kant and transcendental idealism, which would aid us in a post-critical framing of the phenom- ena of post-Kantian philosophical thought, including cosmology, if we  Reading Whitehead 75 wished to undertake the inquiry. But Process and Reality is a book about Modern philosophy and the way it was done from Descartes to Hume —and what it had right. Adventures of Ideas is about Platonic philosophy, seven of its “generalities.” That is what the inquiry is. It is not some other. And so on. Simply to assume that Whitehead’s results in any of his inquiries have automatic application to problems that lie beyond their clearly specified scope is a great mistake. But it is a lamentably common one. To as- sume that the results of Whitehead’s inquiries include ontological knowledge, necessitated by the order of being and the order of know- ing, is to misunderstand completely Whitehead’s method. Philosophical knowledge is not necessary knowledge for Whitehead, although the means by which it is attained will employ necessity internal to the terms of the inquiry itself. 3. Levels of Generality in Process and Reality Another obstacle to understanding Whitehead’s thought has to do with the difficulty many readers have in sorting out the various levels of generality he simultaneously employs in the course of a single inquiry. Apart from the common strategy of genetic and co-ordinate analysis, a Whiteheadian inquiry will be framed by a pair of “bookends,” that is, the most general level of description and the least general (or most particular) level. These levels are adapted to the inquiry at hand, and as the inquiries differ, so do the levels of generality. For the purposes of this chapter, I will make explicit the levels of generality and particu- larity in Process and Reality, but the pattern is the same in every book and even in the essays. It is almost impossible to do any philosophical thinking without moving among various levels of generality. Since Pro- cess and Reality is probably Whitehead’s most important book, and perhaps the most difficult, I will use it as an example. The most general or abstract level of description in PR is the “theory of cosmic epochs,” featuring an account of how “the extensive con- 76 Randall E. Auxier tinuum” is divided in our own cosmic epoch. The extensive continuum itself is conceived as an irreducible undivided divisibility, or a divisible continuum as yet undivided. On a few occasions, Whitehead allows himself to speculate about whether there might be any common rules or characters that would necessarily belong to the extensive continuum in cosmic epochs other than our own, but for the most part the theory of cosmic epochs is intended as a construct that limits the highest ap- plicable level of generality for any human thinking as it inquires in the domain of cosmology. Beyond the constraints and presuppositions found in our own cosmic epoch, we possess no method of inquiry that can be counted on to avoid the pitfalls of vacuous abstractionism. Thus, the “cosmic epoch” is the whole to which all parts belong in the course of PR. The whole is, of course, specified differently in other books. But the cosmic epoch, being the functional limit of inquiry in PR, is func- tionally the universal to which all particulars belong in that inquiry. The first division of the extensive continuum in our cosmic epoch is the temporal division of the continuum, which may be specified in any number of ways, but what is revealed in each mode of temporal divi- sion of the continuum is the genetic divisibility of the continuum itself. However the continuum is temporally divided, the cosmic epoch is designated as the whole to which such temporality belongs, the tempo- ral divisions, no matter how they are specified, being the ultimate character of all parts in the epoch. This, then, is the most general level of description in PR —the theory of cosmic epochs. Whenever White- head uses the term “cosmic epoch,” he is speaking at this level of generality. Other verbal clues have to do with language about “the who- le.” On the other side, the most concrete (or least general or most particu- lar) level of description in Process and Reality is the theory of prehensions (PR 19). Prehensions are “entities” whose mode of exist- ence is described as concrete facts of relatedness. Their “entity” (way of being) is exhibited in the analysis of actual occasions, but they are not found existing independently of an actual entity, nor are prehen- sions independent of one another. In their concrete existing they are the togetherness of the cosmic epoch; prehensions may be treated  Reading Whitehead 77 individually only by an act of abstraction through which real continui- ties are treated as disjuncts. (PR 235) Because prehensions are the most concrete particulars in Whitehead’s inquiry into modern cosmology, they are employed to co-ordinate all the levels of generality in the who- le theory. Thus, prehension stands to cosmic epoch as ultimate part to ultimate whole, hypothetically framing the inquiry. There is no claim that cosmic epochs or prehensions are the ultimate units of the uni- verse itself, only that they will serve the roles of ultimate whole and ultimate parts for the inquiry that is PR. Every inquiry has to specify what whole it takes as its subject matter, and with what concrete parts it will co-ordinate that whole. Between the theory of cosmic epochs and the theory of prehensions in PR are three major levels of generality: (1) the theory of concres- cence and transition, or more simply, the theory of actual entities; (2) the theory of causal efficacy and presentational immediacy, or more simply, the theory of perception; and (3) the theory of propositions and generic contrasts, or more simply the theory of symbolic reference (or even of judgment). These are presented in order, from more general to less general, as the intermediate levels in PR. The theory of judgment is almost as concrete as the theory of prehension, while the theory of actual occasions is almost as general as the theory of cosmic epochs. If some of you find yourselves saying that the theory of actual entities is like Peircean Firstness, the theory of perception is Secondness, and the theory of judgment is Thirdness, I can only say that I would not discourage that kind of creative thinking. But this is not Peircean phe- nomenology. It definitely is metaphysics, and the relations of part and whole are what interest us here. Each of these levels of generality has a view of the whole and the whole is analyzed into “entities” appropriate to each level of generality. Is the “whole,” when analyzed into prehen- sions, the same whole as the whole when analyzed into perceptions? Only by hypothesis, but yes, we do assume it is, even though there is no need to assert its identity or unity in any strict sense. It is more accurate to think of the levels of generality into which the whole may be analyzed as analogous levels. This is how Whitehead speaks, which is another way of saying that we gain in determinateness when we 78 Randall E. Auxier move from more concrete to more general levels, but we lose definite- ness. Even the whole takes on a different character at various levels of gen- erality. For example, the “whole” as articulated by the theory of perception is called “nature,” and its parts are perceptions, their ob- jects, and the forms of relation between these. Taken together, the co- ordinated result of these parts is called “science,” when co-ordinated according to certain kinds of genetic specification (mainly measure- ment), while that same whole is called something like “beauty” when co-ordinated according to certain intensities of organization, exempli- fied in art. The point is that the levels of generality in other of Whitehead’s inquiries, apart from PR, are similar but not identical with those in PR. Past philosophies have made too much of the problem of perception and have tried to get this level of generalization to do more work than it can credibly bear —a problem which persists into the present. This treatment of the structure and levels of generality in PR is brief, but it should be adequate, when taken with the other recommen- dations I have made to serve as a kind of roadmap through the book. I have added an appendix below, using more of the technical terminol- ogy, for those who want to carry the task of reading Whitehead further. 4. Further Applications Below is a discussion that explains in a more advanced way the how and the why of the two major movements in the structure of White- head’s method of inquiry, showing the relation of genetic and co- ordiate division in the phases of inquiry. 4.1. From Extension to Space Elsewhere it has been argued that Whitehead’s concept of “extension” is an irreducible aspect of his metaphysical system, and indeed, this concept of the irreducible extensive continuum is the very source of organicity in the philosophy of organism. Whitehead says:  Reading Whitehead 79 Extension, apart from its spatialization and temporaliza- tion [in the present cosmic epoch], is that general scheme of relationships providing the capacity that many objects can be welded into the real unity of one experience. Thus, an act of experience has an objective scheme of extensive order by reason of the double fact that its own perspective standpoint has extensive content, and that the other actual entities are objectified with the retention of their extensive relationships. These extensive relationships are more fun- damental than their more special spatial and temporal relationships. Extension is the most general scheme of real potentiality, providing the background for all other organic relations. The potential scheme does not determine its own atomization by actual entities. It is divisible; but its real division by actual entities depends upon more particu- lar characteristics of the actual entities constituting the antecedent environment. (PR 67-68) The “more particular characteristics” to which Whitehead here refers are, most importantly, temporal and spatial standpoint1 of a given ac- tual entity. It is easy to lose sight of the repeated claim that time and space are particular to the present cosmic epoch (by hypothesis), and that they supply only one way in which a divisible but undivided exten- sive continuum can be divided. There is no necessity that the extensive continuum be divided according to the determinate orders of time and space, but once this type of order is actual, further conditions are im- posed upon all other actual divisions within their scope (i.e., the present cosmic epoch). If the first division of extensive continuum is temporal, then all spaces will be under the limits imposed by time, and so on. This point establishes the priority and generality of extension for this inquiry, and almost by itself refutes the claim that Whitehead’s mature metaphysics gives priority to what Lewis Ford calls Whitehead’s “dis- 1 The use of the term “perspective standpoint” in this passage is diffi- cult to sort out. At this point it is sufficient to note that Whitehead has distinguished perspective from standpoint just prior to this pas- sage: Perspectives are objectified actual entities as they are available for the percipient actual entity by which they are being felt. The feel- ing of the objectification is not the same as the simple physical feeling of another actual entity by the percipient actual entity. A perspective involves a certain mutuality that a standpoint lacks. (see PR 67, 236) 80 Randall E. Auxier covery” of “temporal atomicity.”1 Ford fails to appreciate that an actual entity simply is a contingent temporal division of the extensive con- tinuum in our own cosmic epoch. All time, and all temporality, so far as it concerns the metaphysics of the present cosmic epoch, is a contin- gent specification of a more general extensive continuum. This is a position Whitehead articulated as early as 1898, restated in explicit terms in the three major works on nature between 1919 and 1923, and never abandoned. The idea of an extensive continuum as a concept of the whole, while variously described in different inquiries, is a constant feature of Whitehead’s philosophy. In PR, time is a contingent specification of extension, and extension is not “space,” it is undivided divisibility. What other modes of division, apart from time and space, might be brought to bear on the extensive continuum, is a question we are not in a position to answer, at least in the domain of cosmology —we have no experience of any non- temporal mode of genetic division beyond our cosmic epoch. But that lack of experience on our part is precisely the reason that time and space must be treated as contingent rather than necessary modes of division. For a radical empiricist such as Whitehead, where evidence is lacking, the very last thing we should do is declare the evidence we have to be “ontologically necessary.” The absence from our experience 1 Ford has been talking about Whitehead's alleged discovery of “tempo- ral atomicity” for many years, and others besides me have challenged his thesis, but his most recent defense of the idea is “The Indispensability of Temporal Atomism,” in Process Studies 38:2 (fall- winter, 2009), 279-303. The argument is also tied up with his equally questionable claim that Whitehead gave up the entire theory of transition in the middle of writing PR, which is not easy to square with the fact that it also appears in AI four years later. As with all of Ford’s defenses, these theses depend on his own imaginative recon- struction of the development of Whitehead’s metaphysics, an account that, even if it turned out to be accurate (which I seriously doubt), would never settle issues regarding Whitehead’s actual views, since the historical genesis of ideas has no necessary bearing upon their subsequent relations to one another. See Ford, The Em- ergence of Whitehead's Metaphysics, 1925–1929 (Albany, NY: SUNY Press, 1984).  Reading Whitehead 81 of other equally primary modes of dividing the extensive continuum is not evidence for the necessity of time and space as its dividers (that is, actual entities), it is rather the best reason to treat them as contingent, and to hold open the possibility of other (as yet unknown) modalities of division. It is not an accident that Whitehead moves directly from the above passage to a long citation from William James. The issue, therefore, to be treated in this appendix is not the irreduc- ible generality of the undivided-but-divisible extensive continuum, but the sense in which time and space, as the modes of division in our cosmic epoch, impose further conditions upon the metaphysical de- scription of the present cosmic epoch. The extensive continuum does not determine the structure of time and space; rather, time and space, that is, actual entities as described in the theory of transition and con- crescence, further divide the continuum in two successive modalities: first, temporal determinations, yielding causal efficacy in perception, and then the spatial division of past from future, which is the space of presentation (or presentational space), and the only conditions under which “contemporaries” can be perceived from any single perspective. Hence time and then space, i.e., actual entities in transition and con- crescence, divide both the continuum and all the relations among the entities they condition in our cosmic epoch. Yet, time and space divide the extensive continuum in two different ways, genetically and co-ordinately. It is easy to become confused about what divisibility and division are. Consider this passage from PR: (P)hysical time or physical space ... are notions which pre- suppose the more general relationship of extension. ... The extensiveness of space is really the spatialization of exten- sion; and the extensiveness of time is really the temporalization of extension. Physical time expresses the reflection of genetic divisibility into coordinate divisibility. (PR 289) In what follows, I will treat in some detail the senses in which genetic divisibility provides a basis for co-ordinate divisibility. Divisibility is not division itself, but a susceptibility of possible division. This is a mode of determinate order (the order of sets of possibilities in their mutual de- terminations) which can be made definite in numerous ways. Genetic 82 Randall E. Auxier divisibility in the present cosmic epoch is the “theory of prehension,” for Whitehead, in the sense that when we consider prehension we have arrived at the way in which all things in the cosmic epoch are con- cretely related, whether negatively or positively, without remainder. Actual division is the task of the actual entity, which is a prehending subject-superject. Prehension includes all the possible modes of division and the generic structure of division itself. Therefore, the theory of prehension can be used to co-ordinate all of the more abstract levels of division. Prehensions do not actually divide the extensive continuum, however; rather, actual entities do that. Prehensions are the entities we discover when we analyze actual entites, and the theory of prehensions then describes how prehensions divide and co-ordinate actual entities. The division of the extensive continuum in our cosmic epoch (time and then space) conditions the further division of the actual entity, the entity that is itself a basic spatio-temporal division of the extensive continuum in our cosmic epoch. To be as clear as I can, I am asserting that prehensions do not do anything, they are entities of possible do- ings, and actual entities, which do divide the continuum are exemplifications of those possibilities of doing. Thus, a theory of pre- hension is both a genetic specification of the types of things that can be done by an actual entity in our own cosmic epoch, and a co-ordination of what they actually do. It is in the first place a theory of divisibility, not of actual division, and only in co-ordination does it move from the possible to the actual. Feelings, which are the content of prehensions, are relational beings, not something that floats around in empty space. The limits upon effected division in the extensive continuum found in the prehending actual entity further determine and condition co- ordinate divisibility. This is to say, in slightly simpler language, that the space of the actual world in our own cosmic epoch just is the highly mediated space of a prehending actual entity. Thus, the most concrete entity, the prehension, is the appropriate entity for the co-ordination of the cosmic epoch itself —whatever order is imposed upon a prehension should be reliably discoverable in all intermediate entities throughout the cosmic epoch (which is another way of saying that an actual entity must be actually somewhere and potentially everywhere in a cosmic  Reading Whitehead 83 epoch). Such mediated space is highly ordered, at numerous levels, and thoroughly determinate. Of all the things it might possibly have been, it actualizes just one set of those possibilities. The limits encountered by prehending actual entities in achieving their satisfactions (and there are many such limits) are conditioning factors upon the space of the actual world of that entity. Each actual entity is, of course, hypothesized to be one standpoint (not perspective) on the cosmic epoch, although this cannot be fully demonstrated; it is assumed. Thus, “extension” is rich in potentiality and “space” is impoverished by comparison. In White- head’s terms: The satisfaction of each actual entity is an element in the givenness of the universe: it limits boundless abstract possibility into the particular real potentiality from which each novel concrescence originates. The ‘boundless ab- stract possibility’ means creativity considered solely in reference to the possibilities of the intervention of eternal objects, and in abstraction from the objective intervention of actual entities belonging to any definite actual world, including God among the actualities abstracted from. (PR 220) On the other hand, space is rich in determination and order, while extension is “chaotic” by comparison, in Whitehead’s peculiar sense of the term “chaos” (see PR 112). The possible intervention of eternal objects upon creativity, considered in abstraction from the objective intervention of actual entities, has a more familiar name: it is called “logic.” The key transition between the extensive continuum and space is ge- netic division, and the most concrete analysis of genetic division is the theory of prehension. The theory of prehension follows a logic that is common to all levels of generality in PR, but is given its exposition in the theory of prehension. The strategy I will adopt in assessing the ways in which genetic division comes to be reflected in co-ordinate division will be to examine the limits exerted by “contrast” and “com- parison” (in Whitehead’s sense), which is the final stage in the theory of judgment, or propositions, with which the theory of prehensions is completed (PR, Part III), and the way opened for the theory of exten- sion (PR, Part IV). 84 Randall E. Auxier The transition between the extensive continuum and its eventual spa- tialization (see PR 220) is genetic division of the continuum by actual entities, and the analysis of genetic division is the theory of prehension. Here, I want to examine the conditioning limits exerted by temporality (or, the temporal determination of the extensive continuum) on the prehending actual entity. Those limits have to do with the ways in which eternal objects ingress, and how the subjective form of a pre- hending actual entity constitutes an indivisible unity conditioning subsequent spatial division. In short, by grasping what, in principle, the actual entity can take in (its transition), and what it must eliminate, we learn both how any actual entity hangs together, and about the deter- minate structure of the space of our cosmic epoch. 4.2. Co-ordinate Division Actually, there are two pages in the corrected edition of PR that have to be visited, pp. 283-284. It is Section I of Chapter I of Part IV, entitled “Co-ordinate Division.” Whitehead has spoken of genetic and co- ordinate division prior to this point, but he has not indicated their full relation. Few students of Whiteheadian thought have ventured into these waters, most of them skipping from p. 280 to p. 337.1 We must grasp where in the course of the inquiry the logic of prehension lies, and why it is situated just there and not elsewhere. After having com- pleted the theory of prehensions in Part III, Whitehead has achieved an outcome, which is a functionally complete description of how an actual entity, in achieving satisfaction, divides the extensive continuum. Thus, the satisfaction is the entire or completed “part” or particular, and it exemplifies a full set of relations (which is the same as to say that it is a unity) to the whole of our cosmic epoch, exhibited at every level of generality, as Part III ends. Thus, as Part IV begins, Whitehead says (please forgive my interpolations in brackets): There are two distinct ways of ‘dividing’ the satisfaction of 1 Jorge Nobo is among those few intrepid interpreters who has stepped into the breach and acquitted himself well. See his Whitehead’s Me- taphysics of Extension and Solidarity (Albany, NY: SUNY Press, 1986).  Reading Whitehead 85 an actual entity into component feelings, genetically and co-ordinately. Genetic division is division of the concres- cence; co-ordinate division is division of the concrete. In the ‘genetic’ mode, the prehensions are exhibited in their genetic relationship to each other. The actual entity is seen as a process; there is growth from phase to phase; there are processes of integration and reintegration [at various levels of generality, such as perception and judgment]. At length a complex unity of objective datum is obtained [that is, the satisfaction], in the guise of a [generic] con- trast of actual entities, eternal objects and propositions, felt with corresponding complex unity of subjective form [that is, the actual entity is a unified togetherness of all these other entities]. (PR 283) Note that the satisfied actual entity, genetically described, comes as an appearance of contrasts between what it actually did in unifying and contributing itself to the world, and the world to which is has contri- buted itself. The contrast is not ultimate precisely because it is and can only be generic. There is no ultimate or final atomization of the whole by the parts, which is to say that we are never in any way raising the question whether the whole is equal to or greater than the sum of its parts. We are simply observing some of the ways in which parts entail, in appearance, the wholes to which they belong, while wholes really do contain their parts. For now the point is only that the contrast of whole and part we achieve in the theory of prehensions is a generic rather than an ultimate contrast. Whitehead continues (and again, my interpo- lations are in brackets): The genetic passage from phase to phase is not in physical time: the exactly converse point of view [that physical time is in genetic passage from phase to phase] expresses the relationship of concrescence to physical time. It can be put shortly by saying, that physical time expresses some features of the growth, but not the growth of the features. The final complete feeling is the ‘satisfaction.’ (PR 283) Obviously this statement further elucidates the cryptic statement, so often quoted by the defenders of the view that Whitehead is a “tempo- ral atomist” that there is a becoming of continuity, but no continuity of becoming. (PR 35) Note carefully that physical time is in genetic pas- sage, not the other way around. Whitehead goes on: Physical time makes its appearance in the ‘co-ordinate’ 86 Randall E. Auxier analysis of the ‘satisfaction.’ The actual entity is the en- joyment of a certain quantum of physical time. But the genetic process is not the temporal succession: such a view is exactly what is denied by the epochal theory of ti- me. (PR 283) Interpreters have taken these lines as confirmation of the primacy of temporal atomism, but they have done so without working through the methodological relation between genetic and co-ordinate division. The very next line provides the needed clue for working through that diffi- cult relationship. The key term is “subjective unity”: Each phase of the genetic process presupposes the entire quantum, and so does each feeling in each phase. The subjective unity dominating the process forbids the divi- sion of that extensive quantum which originates with the primary phase of the subjective aim. The problem domi- nating the concrescence is the actualization of the quantum in solido. (PR 283 first two emphases are mine) Why does “subjective unity” forbid the division of the quantum, and why is the quantum here referred to as “extensive”? Recalling that ex- tensiveness can be divided either temporally or, conditionally, spatially, we have arrived again at the hypothesized irreducible extension of our cosmic epoch. Lest there be any doubt, Whitehead immediately re- minds us that the quantum in question is not only a temporal quantum but also a spatial quantum: “There is a spatial element in the quantum as well as a temporal element. Thus the quantum is an extensive re- gion.” (PR 283) The spatio-temporal quantum, which is another name for the satisfied actual entity, will be treated as a “region” in the final co-ordinate divi- sion. Whitehead further says that the “region is the determinate basis which the concrescence presupposes.” (PR 283) The forbidding of divi- sion of this quantum by its subjective unity, which would be a kind of negation (or elimination of possibilities) for the sake of the solidarity of the actual entity with its actual world, is obligatory in genetic division, in conformity with subjective unity (see PR 26); but that forbidden divi- sion renders hopelessly abstract what it seeks to discover concretely. The prohibition is neither temporal nor spatial in character, it is cate- goreal (i.e., hypothetically presupposed by the terms of this inquiry).  Reading Whitehead 87 This is another way of saying that the satisfied actual entity is in every sense a sufficient “part” of the whole to which it belongs, regardless of how we treat it in our analysis. To allow the genetic division of a satis- faction would be the same as to say that what is finished is not finished, that it is only an abstract but never a wholly concrete part of the whole to which it belongs, its actual world. This violates the soli- darity thesis. For now it is enough to note that something is being forbidden by the requirement of subjective unity, which is a categoreal obligation of genetic division. But co-ordinate division proceeds without regard for the categoreal obligations of genetic division: The co-ordinate divisibility of the satisfaction is the ‘satis- faction’ considered in its relationship to the divisibility of this region. The concrescence presupposes its basic re- gion, and not the region its concrescence. Thus the subjective unity of the concrescence is irrelevant to the di- visibility of the region. In dividing the region we are ignoring the subjective unity which is inconsistent with such division. (PR 283-284, my emphasis) In short, we do not deal with satisfactions qua satisfied when we en- gage in co-ordinate division, and co-ordinate divisibility (not division) was the presupposition of our earlier genetic divisions and their exposi- tion (from perception to judgment). If it were not possible to treat an actual entity as if it were potentially divisible in ways it actually is not divisible, there could be no genetic division. In plainer English, if we could not suppose hypothetically what is actually impossible to do, we could not get an understanding of any concrete part-whole relationship. It is like dissecting a frog, except without harming it —one supposes a dissect-able living frog. Then one provides a description of the main phases of its life, from conception (origination) to death (satisfaction), and then one says “now I have a complete frog.” But one does not because one has supposed a divisible frog whose subjective unity for- bids such division as your genetic account has carried out —in words rather than with sharp knives. Thus, the co-ordinate hypothesis behind the entire inquiry in PR, the philosophy of organism, is a regionalization into extensa of the entities 88 Randall E. Auxier we will exhibit genetically as satisfied actual entities in solidarity with their corresponding actual world. We then further specify those extensa until we have an adequate, applicable, and logically rigorous account of their relations, from whole to part (transition) and from part to whole (concrescence). The ground of this initial move in inquiry, the hypothesis or “as if” character of inquiry is the willingness to take the possible as prior to the actual —not in fact, but in our thinking. Co-ordinate divisibility is a presupposition of our thinking, and genetic division is what provides us with the materials for co-ordinate division, imaginative dissection along multiple planes of experience. We ignore the concrete unity of what- ever is actual when we co-ordinately divide, but we already treated the actual entity as divisible when we entered upon the inquiry. As White- head says, “the region is, after all, divisible, although in the genetic growth it is undivided.” (PR 284) One of the main interests in all this is the role played by possibility. Whitehead continues: “So this divisible [possibility] character of the [actually] undivided region is reflected into the character of the satisfac- tion.” (PR 284) In short, the self-sufficient part with which we ended our genetic account, the satisfied actual entity, is shot through with possibility already —not metaphysically, but because it was treated as a co-ordinately divisible extensum from the start. We don’t as yet know whether the possibility we find in the satisfied actual entity is a function of the inquiry or of the character of the actual entity in solidarity with its actual world. In other language, we don’t yet know whether it must be what it is or whether it simply appears to us as it does as a function of the conditions of inquiry. Thus, as we proceed into co-ordinate divi- sion itself, we must be careful how we understand the results of our efforts. As Whitehead says: When we divide the satisfaction co-ordinately, we do not find feelings which are separate, but feelings which might be separate. In the same way, the divisions of the region [we presupposed at the outset of inquiry] are not divisions which are; they are divisions which might be. Each such mode of division of the extensive region yields ‘extensive quanta’: also an ‘extensive quantum’ can be termed a  Reading Whitehead 89 standpoint. (PR 284) What follows this passage is a rehearsal of a set of logical relations. For our purposes, enough has been said if we now grasp the priority of co- ordinate divisibility, the intervening task of genetic specification, and then the actual carrying out of co-ordinate division itself. We wish to learn something about the relation of possibility to actuality, and we wish to find it not only presupposed but also exemplified in the most general way in our metaphysical descriptions. Only if the exemplifica- tion comes up to the level of what we presupposed in adequacy, applicability and logical rigor, will we have met the demands of our own inquiry. There must be a genetic description of possibility, as it enters into the actual entity’s transition and concrescence, that pro- vides a complete picture of the actual entity in solidarity with its actual world, the world it unifies and enriches. What of this possibility? How can we get at it? In light of what I have discussed above, consider now the following from earlier in PR, while Whitehead is working his way towards a completed description of a satisfied actual entity: “The novel actual entity, which is the effect [of conformal feelings of the present to the past], is the reproduction of the many actual entities of the past. But in this reproduction there is ab- straction from their various totalities of feeling.” (PR 238) That is, we take actual entities out of their own actual worlds and co-ordinate them as elements in the actual world of the actual entity we are analyzing into prehensions. He continues: This abstraction is required by the categoreal conditions for compatible synthesis in the novel unity [in other words, the solidarity thesis]. This abstractive ‘objectifica- tion’ is rendered possible by reason of the ‘divisible’ character of the satisfactions of actual entities. By reason of this ‘divisible’ character causation is the transfer of a feeling, and not of a total satisfaction. The other feelings are dismissed by negative prehensions owing to their lack of compliance with categoreal demands. (PR 238)1 1 If the use of the terms “cause” and “effect” are confusing here, bear in mind that just one page earlier Whitehead said “The reason why the cause is objectively in the effect is that the cause’s feeling cannot, as a feeling, be abstracted from its subject which is the cause. This 90 Randall E. Auxier Negative prehension is the process by which an actual entity eliminates or dismisses (Whitehead uses both terms) those aspects of its actual world which it cannot possibly unify in its satisfaction. The actual entity is under a kind of compulsion here, but the limitations are logical, not ontological. These limits have to do not with what an actual entity is in its actual world, but with the presuppositions we have made in order to analyze an actual entity in its actual world, and to bring a genetic de- scription to completion. More can be (and should be) said, but if I have adequately stressed the complexity of the relations between co-ordinate and genetic divi- sion —how each falsifies experience in an effort to model it, and then offers its resultant model as a clarified version of experience, adapted to purposes we choose, then enough will have been done for the pres- ent. passage of cause into effect is the cumulative character of time. The irreversibility of time depends on this character.” (PR 237) In other words, concretely speaking, we cannot place the actual relations in which we are interested in priority to the merely possible relations we are studying without denying time’s arrow.  III Whitehead’s Cambridge Training Ronny Desmet “Unapplied knowledge is knowledge shorn of its meaning.” Whitehead (ESP 219) 1. Introduction “I have lived three distinct lives in this single span,” said Whitehead to Lucien Price on December 15, 1939; “one from childhood to the first world war; one from 1914 to my residence in America in 1924; and a third here since 1924.” (D 131) Whitehead’s most famous philosophical writings belong to the second and the third stage of his life. However, it would be a mistake to think that these writings can be understood while ignoring the first stage. Each stage of Whitehead’s life integrated the previous one. In this paper I will focus on an early episode of the first stage of Whitehead’s life, his Cambridge training, which, according to me, is of utmost importance to understand Whitehead’s later philosophy of mathematics as well as his later relativistic theory of gravity. Actually, the scope of this paper is more restricted, for it only deals in detail with one aspect of Whitehead’s Cambridge training, the impact of coach Edward Routh and intercollegiate lecturer William Davidson Niven on Whitehead. Biographical details with regard to Whitehead’s Cambridge training can be found in Chapters V and VI of the first volume of Victor Lowe’s Whitehead biography (1985). It is not the aim of this paper to repeat all 92 Ronny Desmet of these details here. Instead of giving a chronological account of the facts constituting the 1880–1884 period of Whitehead’s biography, this paper extensively quotes Andrew Warwick’s Masters of Theory: Cam- bridge and the Rise of Mathematical Physics (2003) to clarify Lowe’s statements that Edward Routh was “the man from whom Whitehead got most of his mathematical training” (97) and that W. D. Niven was the man who “gave Whitehead the most valuable part of his eductation in mathematical physics” (94). In other words, the aim of this paper consists in clarifying, by means of Warwick’s book, and better than Lowe himself has done, what Lowe meant when he wrote: “Routh and Niven gave him most.” (99) The conclusion is that Whitehead learned from Routh and Niven that the analogical application of common mathematical techniques across mathematical physics is the appropriate method, not only to solve a variety of problems in mathematical physics as an undergraduate and graduate student, but also as a researcher after graduation. Moreover, this paper highlights some elements to justify the belief that this con- clusion is important, and that Routh and Niven’s analogical application of common mathematical structures in problem-solving and research can help us to better understand both the particularity of Whitehead’s philosophy of mathematics, and the path of discovery that led to Whitehead’s relativistic theory of gravity. 2. Whitehead’s youth prior to entering Cambridge University Alfred North Whitehead was born on February 15, 1861, in Rams- gate, Kent. The boy, lastborn of four children, was not sent to any school prior to the age of fourteen. He learned his lessons at home, from his father, headmaster of a private school until 1866 or 1867, and clergyman of the Anglican Church until his death in 1898. In September 1875, Whitehead left his father’s vicarage and tutoring to spend five  Whitehead’s Cambridge Training 93 years at Sherborne School, a public school in Dorset, at the opposite end of southern England. At Sherborne, it became obvious that Whitehead’s forte was math- ematics. Whitehead won the school’s Mathematical Medal in 1878, and again in 1879 and in 1880. He also won the Digby Prize for Mathemat- ics and Science three years running. And mid April 1879—his university life was to commence in the autumn of 1880—he went to Cambridge to take Trinity College’s entrance examinations for scholar- ships, and won one. Our story starts when Whitehead’s life as a Cambridge student began the second week of October 1880. I cannot help, however, to briefly add some details concerning Whitehead’s youth in order to avoid the wrong impression that his intellectual life originated solely from explor- ing the landscape of mathematics. His biographer does not fail to emphasize “that in the formation of his mind the land in which, and the shores on which, he grew up played a firm and lasting part” (Lowe 1985:33), and that Whitehead fell in love with Dorset’s country sur- roundings “at the very age when a boy first becomes keenly aware of the beauty of nature.” (46) Also, “Whitehead grew up surrounded by landmarks of ancient and medieval history” (34), and, once in Dorset, “loved to dwell on the presence of the past.” (46) The natural beauty and historical character of the England of his youth was an intimate part of Whitehead’s makeup, and it is at one with the fact that as a schoolboy he developed a major interest in the poetry of Wordsworth and Shelley, and in Thucydides’ account of ancient history. Whitehead was raised as an Anglican in a family of clergymen. This was also an experience that did not fail to impress him deeply, even though, after “a flirtation with Rome” (5) he became an agnostic in the mid-1890s, and after the First World War he gradually developed his own philosophical theism. And yet, the young Whitehead’s interest in religion, poetry of nature, and ancient and medieval history, next to his interest in mathematics and physics, does not say it all. Even though, as Lowe points out, “his adventures were adventures of the mind” (3), 94 Ronny Desmet Whitehead was also part of some—literally—more down to earth activi- ties as a schoolboy. “Being tackled at Rugby, there is the Real,” Whitehead said to William Ernest Hocking in 1934, referring to the fact that he had played rugby at Sherborne. (Hocking 1963:13) In fact, in April 1880, the Shirburnian Magazine described Whitehead as “the best forward the School has ever had.” (Lowe 1985:56) Apart from demonstrating leadership, first as the captain of the Sherborne rugby team, then as the captain of all games played at Sherborne, Whitehead also had to assume leadership responsibility when, in his final year at Sherborne, he was head boy of the entire school, meaning, its overall responsible for discipline outside the class-rooms. This task included one of the most disagreeable things he had to do, whipping other schoolboys for major offences, such as stealing money. 3. The rise of mathematical physics at Cambridge University In October 1880, Whitehead entered Trinity College, Cambridge, and during his four year training, he learned most from coach Edward Routh and intercollegiate lecturer W. D. Niven. Andrew Warwick’s im- pressive study, Masters of Theory: Cambridge and the Rise of Mathematical Physics (2003), is an invaluable source to better under- stand the role of Cambridge educators Routh and Niven in the genesis of Whitehead’s intellectual makeup, and, more specifically, of White- head’s philosophy of mathematics and his relativistic theory of gravity. The rise of mathematical physics at Cambridge is a major example of the increasing professional specialization of the sciences, of which Whitehead wrote: “Another great fact confronting the modern world is the discovery of the method of training professionals, who specialize in particular regions of thought.” Whitehead did not only stress “the suc- cess of this professionalising of knowledge,” but also “the dangers arising from this aspect of professionalism.” (SMW 196-197) However,  Whitehead’s Cambridge Training 95 instead of turning to the dangers listed by Whitehead mid 1920s, let us turn to the nineteenth century emergence of mathematical physics as the professional activity of specialized scientists—notice that “by an- alogy with artist” (Yeo 2002:61), the term ‘scientist,’ “with its resonances of professional specialization, was only introduced (by […] William Whewell) in 1834.” (Harman 2002:1) According to Andrew Warwick, there were two lines of development during the seventeenth century that ultimately (in the nineteenth cen- tury) led to the emergence of mathematical physics as a professional discipline: “The first was the gradual abandonment of the search for the causes of physical phenomena in favor of the mathematical certainty of what was know from the early seventeenth century as ‘physico- mathematics.’” (28) The publication of Newton’s Philosophiae Naturalis Principia Mathematica (1687), generally known as Principia, was an important high point of this evolution. “The second and related line of development was the invention of the mathematical methods that would eventually lie at the heart of math- ematical physics. Foremost among these were the algebra of François Vièta, the algebraic geometry of Descartes and Pierre Fermat, and the differential and integral calculus developed independently by Newton and Leibniz.” (28-29) Warwick points out that these tools formed the basis of the eighteenth century mathematical ‘analysis,’ but does not fail to stress that, “despite its beginnings in the decades around 1700, it was only during the eighteenth century that many of the mathematical methods and physical principles now associated with classical mechan- ics began to emerge.” (29) After listing methods such as Euler’s for solving differential equations, and physical principles such as the principle of least action, Warwick adds: These methods were formalized, further developed, and systematically expounded in the decades around 1800 in such great treatises as Joseph Louis Lagrange’s Mécanique analytique (1788) and Pierre-Simon Laplace’s Traité de mécanique céleste (1798–1827). In the early decades of the nineteenth century a clear recognizable discipline of mathematical physics began to emerge as these methods 96 Ronny Desmet were applied by men like Joseph Fourier, Augustin Fres- nel, and Georg Ohm to such terrestrial phenomena as heat, optics, and the electrical circuit. (29-30) Most mathematicians named by Warwick in the last quote are French—Ohm being the exception. At Cambridge, prior to the nine- teenth century, French (and German and Italian) analytical methods played a less prominent role in mathematical education than Newton’s works, the Principia and the Optics (1704). Newton has rightly been called the “creator of the Cambridge scientific tradition.” (Hall 2002:36) However, according to Warwick, some of Newton’s clerical disciples used his work in the early decades of the eighteenth century “to build an alliance between Newtonian natural philosophy and Anglicanism,” and hence, “initially, it was the more qualitative natural theological aspects of Newton’s work that were emphasized.” (57) So, at Cam- bridge, “it was originally in the form of natural theology that Newton science entered undergraduate studies,” but gradually “more technical aspects of his mathematics and mechanics began to be emphasized.” (118) Warwick deals with several, closely linked factors to explain how, dur- ing the eighteenth and nineteenth century, ‘mixed mathematics’ (geometry, arithmetic, algebra, calculus, mechanics, hydrostatics, op- tics, and astronomy) began to displace more traditional subjects at Cambridge, such as theology and moral philosophy. I list three of these factors, each contributing to the ninetheenth centrury rise of math- ematical physics at Cambridge. The first factor was the establishment, in the 1750s, of the Math- ematical Tripos at Cambridge. The term ‘Tripos’ was used to denote ‘examination,’ but originally, it had been applied to “the three-legged stool on which a Bachelor of Art sat to dispute with candidates for de- grees.” (Lowe 1985:78) “From the mid-eighteenth century,” Warwick writes, “competitive, written examinations replaced the Latin disputa- tions as the dominant form of student assessment” (37), and “with the rise of competitive, written examinations and the strict ranking of stu- dents by marks, the emphasis began to shift towards the technical content of the Principia. The discipline of mathematics was especially  Whitehead’s Cambridge Training 97 well suited to an examination that sought to discriminate between the performances of large numbers of well-prepared students. Unlike ques- tions in theology and moral philosophy, those in mathematics could be made more and more difficult as the examination proceeded and be straightforwardly assessed according to a scheme of marks.” (57-58) The Mathematical Tripos examination at Cambridge extended over several days, and based on their marks, the participating students were divided into three classes, the highest being ‘Wranglers,’ followed by senior and junior ‘optime,’ while the remainder were called the ‘hoi polloi’ (majority) or simply ‘poll men,’ and were deemed unworthy of honors. The highest honor for a student was to become the Senior Wrangler—the best of the first class students. As David Wilson makes clear (cf. Wilson 1982:334), by the time Whitehead took the Mathematical Tripos examinations at Cambridge, it was customary for a student to prepare nine terms (three years) for Parts I and II of the Mathematical Tripos (both examination parts lasted three days, one shortly after the other), and one additional term for Part III (lasting another three days). Whitehead became Fourth Wran- gler in June 1883, based on his Part I and II marks (G. B. Matthews was Senior Wrangler, E.G. Gallop Second, and Robert Lachlan Third; the fact that John Chevallier and Whitehead were bracketed Fourth, might ex- plain why Wilson wrongly lists Whitehead as Fifth Wrangler—cf. Lowe 1985:103 and Wilson 1982:362). And Whitehead was one of seven who made First Class (no further order of merit was given) in January 1884, based on his Part III marks (cf. Lowe 1985:104-105). Notice that prior to 1882 students prepared for three years, then took the Math- ematical Tripos exam (in two parts), and then, shortly after the Mathematical Tripos, the top Wranglers had an opportunity to obtain further distinction by competing in a final examination for the first and second Smith’s Prizes. As it was almost excluded that a student was able to successfully pre- pare for it on his own, the introduction of the Mathematical Tripos increased the importance of private tutoring at Cambridge. Warwick writes: 98 Ronny Desmet An important aspect of this enormous expansion in mixed-mathematics studies is that it represented a major change not just in what was taught but also in how and by whom it was taught. […] Mathematics could not easily be learned from formal lectures, oral debate, and reading alone. In order rapidly to master complicated mathemati- cal methods and their application to difficult physical problems, the vast majority of students needed an ordered and progressive plan of study, long periods of private re- hearsal tackling graded examples on paper, and regular face-to-face interaction with a tutor prepared to correct their written work, explain difficult concepts and tech- niques, and demonstrate good practice. In Cambridge the latter function was fulfilled not by college lecturers or uni- versity professors, but by private tutors (usually college fellows) who were prepared to manage a student’s studies for a fee. (37) Once it became clear to students that success at Cam- bridge depended upon their ability to reproduce mathematical knowledge on paper and to solve difficult mathematical problems, they began to turn in increasing numbers to private tutors who were willing and able to explain the technical content of such difficult books as Newton’s Principia and to drill them individually in the problem-solving techniques they had to master. (58) Moreover, with the introduction of the Mathematical Tripos, “paper- based techniques of calculation began routinely to be employed in un- dergraduate study,” and Warwick adds: Prior to this, mathematical education, like other branches of study institutionalized in the medieval university, was based mainly on private reading, oral debate, and cate- chetical lectures. The introduction of paper-based mathematical study gradually displaced these long- established pedagogical traditions, instituting instead tough regimes of competitive technical training. An im- portant aspect of these regimes was the requirement that students be able […] to solve difficult mathematical prob- lems on paper. This aspect of the shift from oral to written study represented much more than a mere change of me- dium by which mathematics was learned. Paper-based problem solving had hitherto been a technique employed by those engaged in original mathematical investigations, and many of the problems […] that gradually became standard student exercises were ones that had originally challenged the greatest mathematicians […] The introduc- tion of paper-based learning and examination therefore  Whitehead’s Cambridge Training 99 marked a major and profound period of cultural transfor- mation in the history of the exact sciences, during which the working practices used by the founders of modern mathematical physics became central to undergraduate training in the universities. (116-117) A second factor to explain the rise of mathematical physics at Cam- bridge, according to Warwick, “probably lies in the appearance in the 1740s and 1750s of a large number of introductory treatises on the fluxional calculus,” and: Although it was Newton who had originally invented and developed the fluxional calculus, he neither published an introductory text on the subject nor showed how it could be systematically applied to physical topics in natural phi- losophy. In the first half of the eighteenth century, Newton’s mechanics and theory of gravitation was there- fore taught in Cambridge in the geometrical form in which it was presented in the Principia, while optics, astronomy, pneumatics, and hydrostatics were generally taught as qualitative and experimental subjects. The new books which appeared in the mid-eighteenth century offered a systematic introduction to the fundamental operations of the fluxional calculus and showed how it could be applied to the solution of a wide range of mathematical and phys- ical problems. […] The strongly problem-oriented presentation in the treatises […] made it much easier for university students to master the fluxional calculus and its applications, helped to define a new field of mixed- mathematical studies, and provided Cambridge examiners with a ready supply of standard problems. (118-119) Despite the increasing importance of the differential and integral calcu- lus (first in the British, Newtonian format, and later on, in the continental, Leibnizian format), more than a century later, in the 1880s, when Whitehead was a Cambridge undergraduate, “throughout Part I of the Tripos, use of the calculus was prohibited.” (Lowe 1985:101) In Part I of the Mathematical Tripos exam, an undergraduate was limited to the purely geometrical methods of the Principia, and only in Parts II and III a student was allowed to show his mastery of the differential and integral calculus. This can be illustrated by summarizing the content of the Mathematical Tripos exam that Whitehead took (for more details, cf. Wilson 1982:367-369 and Lowe 1985:100-101). 100 Ronny Desmet Part I covered Euclid and the first three sections of Book I of Newton’s Principia, as well as the elementary parts of arithmetic, algebra, trigo- nometry, conic sections, statics, dynamics, hydrostatics, optics, and astronomy. Part II covered advanced parts of Part I subjects, as well as analytical geometry (including curvature of curves and surfaces), differ- ential and integral calculus, differential equations, and attractions and potentials. Part III, divided in four groups of subjects, covered some more sections of Book I of the Principia, and advanced parts of Part II subjects, as well as the calculus of variations, finite differences, elliptic and other special functions, chance theory, lunar and planetary theo- ries, figure of the earth, precession and nutation, sound and vibrations of strings and bars, hydrodynamics (including waves and tides) and elastic solids, expressing functions by series or integrals involving sines and cosines, conduction of heat and thermodynamics, electricity and magnetism. A third factor to explain the rise of mathematical physics at Cam- bridge, and its development into a truly professional discipline, is formed by the gradual, nineteenth century introduction at Cambridge of the analytical methods developed by continental mathematicians, and, closely related, by the complete takeover of undergraduate teach- ing by private tutors. William Whewell, the man who coined the term ‘physicist,’ is one of the men responsible for the introduction at Cambridge of continental, analytical methods. Whewell, nowadays remembered as “a Cambridge historian and philosopher of science” (Yeo 2002:51), was born in Lan- caster in 1794, and died in Cambridge in 1866. According to Richard Yeo, “Whewell was a product of the Mathematical Tripos […] Graduat- ing as Second Wrangler in January 1816, Whewell displayed the mental ability—and physical endurance—tested by the Tripos exam.” (54) Warwick writes on Whewell: Whewell began his career as a private mathematics tutor and proceeded, via a fellowship at Trinity and the profes- sorships of mineralogy and moral philosophy, to the mastership of Trinity in 1841. As a student and young mathematics tutor, Whewell had recognized the import- ance of French analysis, especially in establishing new  Whitehead’s Cambridge Training 101 results in mechanics, and initially participated in the introduction of the new methods. His textbooks on me- chanics and dynamics […] introduced students to the [Leibnizian] d-notation calculus [e.g., his 1823 Treatise on Dynamics provided a concise guide to dynamics in ana- lytical form], but Whewell remained close to traditional geometrical methods whenever possible and always pre- sented analysis as a useful tool in solving physical problems. (95) Notice that Warwick emphasizes Whewell’s initial promotion of the new methods, as well as his remaining closeness to the traditional geometrical methods. This ambivalence points at the nineteenth cen- tury tension between analytical calculation and geometrical reasoning. This tension in mathematics between the analytic and the synthetic style is closely related to, and grew into, the tension between adherents of formal (or pure) mathematics, and adherents of descriptive (or ap- plied) mathematics, as described by Joan Richards in Mathematical Visions: The Pursuit of Geometry in Victorian England (1988). Both Richards and Warwick make clear that Whewell’s defense of traditional geometrical methods was part of his defense of the traditional educa- tional values of Cambridge University. Warwick writes: “For Whewell, the prime purpose of the study of mathematics in the university was not to train professional mathematicians and foster research in pure analysis, but to form the basis of a liberal education for the intellectual elite. The purpose of a liberal education, he argued, was ‘to develop the whole mental system of man.’” (95) Whewell’s protest against the professional specialization of math- ematics, and his conservative defense of geometrical reasoning, next to his innovative introduction of analytical methods for mathematical problem-solving, are comparable to Whitehead’s later warning against the dangers of professional specialization, and his conservative defense of applied mathematics, next to his innovative contributions to the development of pure mathematics. A number of nineteenth century Cambridge men—e.g., William Hopkins—were less ambiguously in favor of teaching new mathematical methods than Whewell was, and similarly, a number of early twentieth century Cambridge men—e.g., 102 Ronny Desmet Bertrand Russell and G. H. Hardy—were more univocal promoters of pure mathematics than Whitehead was. I should not, however, stretch this Whewell-Whitehead parallelism too far. This paper does not deal with Whitehead’s role as an educator, but Lowe’s biography and Whitehead’s own writings on the subject of edu- cation (e.g., AE) prove that Whitehead has been a more open-minded and progressive educational reformer in the first half of twentieth cen- tury than Whewell in the nineteenth century. In the context of the difference between Whewell and Whitehead qua open-mindedness, it is relevant to quote the following, funny passage from Whitehead’s Modes of Thought: There is a rhyme which fits onto the tradition respecting Dr. Whewell, who was Master of Trinity College, Cam- bridge, about eighty years ago. The rhyme is well-known and runs thus: I am Master of this College; And what I know not, Is not knowledge. This attitude is always prevalent in the learned world. It sterilizes imaginative thought, and thereby blocks pro- gress. In our discussion of understanding, this is the first heresy that I wish to combat. I am not attributing this heresy to Dr. Whewell, although he is said to have exhibited an ar- rogance, perhaps justified by his very extensive learning. My point is that understanding is never a completed state of mind. It always bears the character of a process of pen- etration, incomplete and partial. (MT 43) Next to the role played, in the eighteenth century, by the introduction of paper-based learning and examination, and by the reconstruction and application of Newton’s method of fluxions, the gradual introduc- tion in the nineteenth century of continental analytical methods played an important role in the increasing importance and difficulty of math- ematical problem-solving, and in the professional specialization of mathematical physics at Cambridge University. The increasing importance and difficulty of mathematical problem- solving, according to Warwick, “contributed to the complete takeover  Whitehead’s Cambridge Training 103 of undergraduate teaching by private tutors during the latter 1820s and 1830s” (149), and he writes: During the first third of the nineteenth century, these tu- tors assumed complete responsibility for preparing the most able undergraduates for increasingly difficult and competitive written examinations in mixed mathematics. Their success as teachers was based on the power of the pedagogical methods they developed to impart their pupils a very high level of technical skill over a relatively short period of time. […] This pedagogical revolution marked a major watershed in both the nature of undergraduate stud- ies and in the development of the mathematical sciences. (37-38) Warwick holds that this revolution was “a remarkable revolution in training that brought the modern mathematical physicist into being” (38), and that the significance of this revolution was “neatly captured circa 1830 in the term ‘coach.’” (40) In order to grasp that significance, Warwick writes: It is important to understand that in the decade immedi- ately preceding the widespread building of railways, the latest stage and mailcoaches, running on newly Macada- mized road surfaces, represented the most exciting and rapid form of modern transport. These were the years when the coach, rather than the train, was the icon of progressive transport, and the generation of young men growing up in the 1820s and early 30s were highly ‘coach conscious,’ associating coaches and coachmen with speed, adventure, and—unlike the trains that replaced them for long-distance travel in the late 1830s and 40s—privilege and wealth. […] These perceptions of coaches and coach travel help us to appreciate the qualities that mathematics students sought to make visible and gently ridicule in their tutors. The tutor, like the coachman, drove his pupils along a predetermined course even when they felt inclined to stray or slack. This quality was complemented by the use of the term ‘team’—from team of horses—to describe the students working with a particular coach. Another, more subtle yet equally important quality possessed by coach- man and tutor was the ability to convey a team from A to B unnaturally fast by skilful driving and the careful design of the path traversed. […] Private tutors carefully designed a whole apparatus of progressive tuition which, like stage- coach and road, enabled the student to proceed much more rapidly than he could by his own unaided efforts or 104 Ronny Desmet even with the help of traditional lectures. (89-90) I am giving this extensive Warwick quote on the etymology of the terms ‘coach’ and ‘team,’ because his account of the origin of these Cambridge terms provides a nice example of the age-old metaphorical innovations characteristic of our natural language, which prefigure the modern analogical innovations characteristic of mathematical physics in general, and of Whitehead’s relativistic theory of gravity in particu- lar. Anyway, jumping from the 1830s to the 1880s, Whitehead, when he was a student at Cambridge preparing for the Mathematical Tripos, turned to a coach too, and not just any coach, but, according to Lowe, “the greatest in the series of great coaches […] in Cambridge.” (98) I am referring to Edward Routh, and will deal with him in the next sec- tion. 4. Coaching by Edward Routh Edward Routh was born in Quebec in 1831, and he died in Cambridge in 1907. Routh came to England at the age of eleven. He attended Uni- versity College School and then, having won a scholarship, he entered University College, London, at the age of sixteen. At University College he was taught by Augustus De Morgan, “under whose tutelage he em- erged as a brilliant mathematics student.” (Warwick 2003:231) Routh obtained his B.A. (1849) and M.A. (1853) in London. After winning an exhibition, he entered Peterhouse College, Cambridge, in 1850, and was coached first by Isaac Todhunter and then by William Hopkins for the Mathematical Tripos of 1854. Routh came out Senior Wrangler, beating James Clerk Maxwell into second place. The two young math- ematicians subsequently shared the Smith’s Prize. When the leading coach and lecturer at Peterhouse, W. J. Steele fell ill, Routh took over his private pupils and college lectures, and according to Warwick, “it quickly became evident that Routh was an outstanding exponent of the coaching methods pioneered by Hopkins.” (232) Routh’s temporary  Whitehead’s Cambridge Training 105 replacement of Steele turned into a permanent job after Steele’s death and Routh’s election to a fellowship and lectureship at Peterhouse in 1855. In the Times obituary of Routh (June 8, 1907) we can read: “He adopted teaching as his profession, and became the pre-eminent ‘coach’ all the world knew of. Between 1855 and 1888 he trained out of about 700 pupils 500 Wranglers, 27 being Senior Wranglers and 41 Smith’s Prizemen.” The following quotes make obvious that Andrew Warwick values Routh’s qualities as a coach as high as Victor Lowe. Like Lowe, Warwick calls Routh “the greatest of all the Cambridge coaches” (228), and he continues: Routh was by far the most successful of all the Cambridge coaches and was probably the most influential mathemat- ics teacher of all time. (231) Routh was by far the most influential mathematics teacher in mid and late Victorian Britain. (232) Routh’s career from the early 1860s to the late 1880s marked the high point of coaching in Cambridge. In no other major center of mathematical education, before or since, has one man exercised such comprehensive control over undergraduate training. (239) Edward Routh’s practice of teaching mathematical methods in close association with their physical applications did not only impress histor- ians like Lowe and Warwick, but contemporaries as well. Warwick writes: For example, the great German mathematician and leader of the Göttingen school, Felix Klein, was extremely im- pressed by what he saw as the close and productive relationship nurtured in Cambridge between the develop- ment of mathematical methods and their application to problems in mathematical physics. […] A regular visitor to Cambridge, Klein made a special study of mathematics teaching in the university in an explicit attempt to under- stand ‘why English mathematical physicists had so much practical command over the application of their know- ledge.’ He specifically identified Routh’s training methods as the key to this special faculty and decided that the most practical way of making Routh’s approach accessible to a Continental audience would be to commission a German translation of Routh’s Dynamics of a System of Rigid Bod- ies (1868). (252-253) 106 Ronny Desmet In November 1882, in the Preface of the fourth, revised and enlarged edition of Part I of this Dynamics, Routh wrote: “I cannot conclude without expressing how much I am indebted to Mr. A. N. Whitehead and Mr. E. G. Gallop of Trinity College for their assistance in correcting many of the proof sheets. It is hoped that the work, having had the advantage of their revision, will be found clear of serious errors.” (vii) This suggests that in the fall of 1882, Whitehead must have been one of Routh’s best advanced third year students. As a matter of fact, “White- head gave Trinity College good evidence of his progress toward wranglership when taking the annual college examination for honor students in the spring of 1882. […] The five-day examination was set- up, like the Tripos, as a writing race. There were so many problems to be worked that no mere human could come anywhere near making a perfect score. That would have been 1400 points; no one but White- head (with 735) and Gallop (with 774) topped 600.” (Lowe 1985:100) The 1882 Preface of Routh’s Dynamics is one of the three pieces of evidence that led Lowe to conclude that Whitehead was a pupil of Routh. According to Lowe, no list of Routh’s pupils from 1880 to 1883 seems to exist, and hence Lowe needed indirect evidence. Next to Routh’s Preface, Lowe found two other items of such evidence. An article on page ten of the London Times of June 11, 1907, mentions that Whitehead was one of thirteen who represented the Royal Society at Routh’s funeral service. Also, in 1923 (and not in 1924, as Lowe writes), when explaining his reserve with regard to Einstein’s general theory of relativity at the Physical Society of London, Whitehead em- ployed a metaphor used by Routh in one of his lectures. Here is what Whitehead said: In investigating the laws of nature what really concerns us is our own experiences and the uniformities which they exhibit, and the extreme generalizations of the Einstein method are only of value in so far as they suggest lines along which these experiences may be investigated. There is a danger in taking such generalizations as our essential realities, and in particular the metaphorical ‘warp’ in space-time is liable to cramp the imagination of the physi- cist, by turning physics into geometry. The case is a little like that of a metaphor used by Dr. Routh in lecturing on metacentres. He would draw a ship on his hand in chalk  Whitehead’s Cambridge Training 107 and rock it, and then explain that ‘you now remove the sea.’ (Temple 1923:193) When, in 1923, Whitehead said that the extreme generalizations of Einstein’s tensor method are of value in so far as they suggest lines of research along which the uniform texture of our experiences can be investigated, he referred to the line of research which includes Ludwik Silberstein’s 1918 article, “General Relativity without the Equivalence Hypothesis,” Whitehead’s own 1920-1922 relativistic theory of gravity, and George Temple’s 1923 constantly curved space-time alternatives— the topic of discussion at the Physical Society in London when White- head attended and explained his divergence from Einstein as quoted above. When Whitehead warned the members of this society against taking extreme generalizations as essential realities, he formulated what he was going to denounce, two years later, as the “Fallacy of Mis- placed Concreteness”—the “error of mistaking the abstract for the concrete.” (SMW 51) And when Whitehead rejected Einstein’s meta- phorical warps of space-time, and the allied move to turn physics into geometry, he reiterated his 1922 rejection of Einstein’s “geometrical metaphors,” and reconfirmed “the old division between physics and geometry.” (R v-vi) However, I am giving the above 1923 quote to point at the fact that Routh was Whitehead’s coach, and that, according to me, it is no co- incidence that Whitehead remembers Routh as giving a metaphor. Routh’s use of metaphors and analogies was an important aspect of his teaching of mathematics via physical applications. If asked what Whitehead learned “by hearing and watching a brilliant coach talk and chalk his way through problems and examples on a blackboard” (War- wick 2003:228), my answer is: “the analogical application of common mathematical methods.” (Idem 278) And if I add that “students trained to solve mathematical problems took problem-solving as a model for research after graduation” (Idem 229), I come close to what will be my conclusion with regard to Whitehead’s Cambridge training, that it is the analogical application of common mathematical structures in the prob- lem-solving approach characteristic of nineteenth century Cambridge in general, and of Routh in particular, which can help us to better under- 108 Ronny Desmet stand both the particularity of Whitehead’s philosophy of mathematics, and the path of discovery of Whitehead’s relativistic theory of gravity. I close this section with another long, but, in the context of this paper, one of the most relevant quotes from Warwick’s Masters of Theory, stressing the importance of analogies, and mentioning, as examples of the common mathematical methods and principles across analogous applications, two core notions of Whitehead’s relativistic theory of gravity. Warwick underscores that in attending Routh’s lectures, study- ing his treatises, and solving Tripos problems, Routh’s pupils were learning the methods and techniques that might be useful in a research career, and Warwick adds: One final aspect of the problem-solving approach to mathematics that was of special significance to wrangler research is the technical unity lent to mathematical phys- ics by the analogical application of common mathematical methods. Several historians have remarked upon the deep commitment to dynamical explanation displayed by Cam- bridge mathematical physicists in the last third of the nineteenth century, but it is important to appreciate that this was as much a commitment to a range of techniques for tackling problems as it was to an ideology of mecha- nistic explanation. For example, […] coaches such as Routh […] spent a good deal of time drilling their pupils in the solution of Laplace’s equation. The reason for this was that the concept of ‘potential’ was one that could be ap- plied not just to gravitational theory and the various branches of mechanics but to thermodynamics, electro- statics, magnetostatics, and electromagnetism. Having learned a range of techniques for solving problems in, say, gravitational potentials, a coach could introduce a new topic such as electrostatics by developing the analogy be- tween gravitational and electrostatic potential theory. Likewise Lagrangian dynamics and the principle of least action were powerful methods precisely because, although dynamical in origin, they could be applied to numerous physical phenomena while making only very general as- sumptions regarding the mechanical nature of the micro- processes involved. Undergraduate training thus encour- aged […] young researchers […] to reduce the physical world to Tripos-like problems. To accomplish this goal they had to establish similarity relations between tractable and currently intractable phenomena using laws, princi- ples, and mathematical methods they had been taught to  Whitehead’s Cambridge Training 109 take for granted. A problem-based training was especially useful in this process because it provided a ready supply of analogical examples.” (278-279) When Warwick stresses that the deep Cambridge commitment to dy- namical explanation (as exhibited, e.g., by Maxwell) was as much a commitment to the analogical application of a range of common math- ematical techniques as it was to an ideology of mechanistic explanation, his statements can be read as an antidote and corrective to Pierre Duhem’s anti-British and reductive interpretation of this commitment as a strong and exclusive adherence to mechanical mod- els. (Cf. Duhem’s 1914 edition of The Aim and Structure of Physical Theory) It is interesting to link Warwick’s correction of Duhem to yet another element in the history of the philosophy of science. In the 1960s, Mary Hesse revalued the role of analogical thinking in science, and wrote Models and Analogies in Science. (For a more recent account of the role of analogical thinking in science, see Nersessian 1984 & 2008.) In her book, Hesse contrasts Duhem with Norman Robert Campbell, the author of Physics, the Elements (1920), by means of a dialogue on the function of models between a “Duhemist” and a “Campbellian.” (Hesse 1966:7-56) The link between Warwick and Hesse is clear at once when adding the fact that Campbell was a pro- duct of Cambridge training, fellowship, and research, and hence, that he was the appropriate source for Hesse to stress that analogical think- ing in science involves as much mathematical modeling as it involves mechanical modeling. And this brings us back to Whitehead, whose philosophy of nature is characterized, both by mathematical modeling (e.g., his development of alternative mathematical models of the ma- terial world in MCMW, and his extensive abstraction of space-time from the perceptual manifold of events in PNK and CN), and by anti- mechanistic motives (e.g., his rejection of the traditional ether in MCMW, and his revolt against the matter/mind bifurcation of nature in CN). Indeed, the Cambridge experience of the unity lent to mathematical physics by the analogical application of common mathematical struc- tures is one of the most important factors that ultimately, at the end of 110 Ronny Desmet his Cambridge career in 1910, led Whitehead to write: “Every branch of physics gives rise to an application of mathematics. A prophecy may be hazarded that in the future these applications will unify themselves into a mathematical theory of a hypothetical substructure of the universe, uniform under all the diverse phenomena.” (ESP 285) This statement is a key to better understand the particularity of Whitehead’s philosophy of mathematics. Moreover, the application, by analogy with electro- magnetism, of the notions of ‘potential’ and ‘least action’ in Whitehead’s non-mechanistic solution to the problem of finding a rela- tivistic law of gravitation, is one of the major factors in Whitehead’s discovery of an alternative for Einstein’s general theory of relativity in the early 1920s. In other words, it is a key to better understand White- head’s relativistic theory of gravity. 5. Intercollegiate lecturing by W. D. Niven Next to Edward Routh, another Cambridge man played a major role in Whitehead’s training as a mathematician, W. D. Niven. I introduced Routh in the context of the takeover of undergraduate teaching by coaches during the 1820s and 1830s. In order to introduce Niven, I have to give a short account of the gradual reform of public lecturing at Cambridge, which challenged the dominance of private coaching dur- ing the 1860s and 1870s. (Cf. Warwick 2003:264-272 and 280-285) In the early 1850s, contrary to William Whewell, who defended mathematical studies as the best means to develop the whole mental system of man, William Hopkins campaigned to make the mathemati- cal studies more relevant to the commercial and industrial interests of the British nation. During the subsequent decade, two Cambridge graduates, William Thomson (the later Lord Kelvin, Second Wrangler and Smith’s Prize winner in 1845) and James Clerk Maxwell (as said before, Second Wrangler and Smith’s Prize winner in 1854) combined brilliant theoretical investigations with both experimentation and par- ticipation in such major industrial projects as submarine telegraphy, hence realizing Hopkins’s vision. In line with Hopkin’s response to the  Whitehead’s Cambridge Training 111 new educational demands and expectations generated by the industrial revolution, and inspired by Thomson and Maxwell’s achievements, in the mid 1860s, several prominent Cambridge-trained mathematicians, led by the Astronomer Royal, George Airy, urged that the major new topics of thermodynamics, electricity, and magnetism be included in the Mathematical Tripos exam. Of course, one could not just add these new subjects to the Math- ematical Tripos syllabus. At least two prior problems needed to be solved. One: The coaches offered a complete course of study, which prepared students for every topic of the Mathematical Tripos syllabus, but no single teacher could claim to master all the advanced and new subjects. Moreover, the average college lecturer was no better placed than the average coach to teach the new subjects. Two: These topics could not be taught properly without practical demonstrations of the major instruments and experiments involved. Consequently, in the late 1860s and 1870s, a number of reforms took place, leading to an up- dated Mathematical Tripos syllabus, to intercollegiate and university lecture courses, given by specialists in the advanced and new subjects, and to the creation of the Cavendish Laboratory. James Clerk Maxwell played his part in these reforms, namely, as an examiner and moderator for the Mathematical Tripos, as the writer of an advanced textbook on electricity and magnetism, his Treatise on Electricity and Magnetism (1873), and as the new Professor of Experi- mental Physics, requiring him to offer public lectures on heat, electricity and magnetism to Mathematical Tripos students, and to de- sign and direct the new Cavendish Laboratory that opened in 1874. (Cf. Harman 1998:68-69 and Warwick 2003:286-287) By the time that Whitehead had to study advanced topics at Cam- bridge, a few years after Maxwell’s untimely death in 1879, the conduction of heat, thermodynamics, electricity, and magnetism, formed the bulk of the fourth group of advanced topics of Part III of the Mathematical Tripos syllabus; the new division of pedagogical labor between private coaches and public lecturers—intercollegiate or univer- sity lecturers—was established, the former providing all-round 112 Ronny Desmet mathematical training upon which the latter could build to provide specialized training; and top wranglers were referred by coaches and lecturers to three, by then standard, textbooks: William Thomson and P. G. Tait’s Treatise on Natural Philosophy (1867), Maxwell’s Treatise, and Lord Rayleigh’s Theory of Sound (1877). The Treatise by Thomson and Tait (like Thomson and Maxwell, Sec- ond Wrangler and Smith’s Prize winner, but in 1852) “quickly became an important reference work in Cambridge,” and it was referred to “as the definitive introduction to vibration theory, hydrodynamics, the shape of the earth, potential theory, harmonic analysis, and, most im- portantly for the establishment of mathematical physics in Cambridge, Lagrangian and Hamiltonian dynamics, and the principle of conserva- tion of energy.” (Warwick 2003:292) Maxwell’s Treatise was largely written “as an advanced textbook on the mathematical theory, instrumentation, and experimental founda- tion of electricity and magnetism, and included an account of [Maxwell’s] new field-theoretic approach.” (Idem 287) “Maxwell’s book was certainly read by many individuals throughout Britain during the 1870s”—three of whom, G. F. FitzGerald, Oliver Heaviside, and Oliver Lodge, were most important for the development of electromagnetism (cf. Hunt 1991)—“but only in Cambridge in this period was the Treatise used to train a substantial number of students in electromagnetic field theory.” (Warwick 2003:288) The Theory of Sound by Rayleigh (Senior Wrangler and First Smith’s Prizeman in 1865, and second Cavendish Professor of Experimental Physics, following Maxwell in 1879) “provided an exceptionally fruitful source of new physical imagery and mathematical methods to several wranglers developing electromagnetic theory in the late 1870s and 1880s. Rather like the approach to the science of electromagnetism adopted by Maxwell in the Treatise, the Theory of Sound offered a gen- eral overview of recent work in the mathematical theory of acoustics as well as a systematic statement and development of Rayleigh’s own research in this and related subjects. Rayleigh’s book was actually a much more ambitious and far-reaching study than the modest title  Whitehead’s Cambridge Training 113 implied […] there was virtually no vibrating system that could not be tackled successfully using the techniques developed by Rayleigh in the first ten chapters.” (Idem 324) In his article, “A. N. Whitehead Natural Philosopher,” Jacques Riche correctly conceives Thomson and Tait’s book as part of Whitehead’s background (Riche 2006:29-30), and the same can be done with regard to Rayleigh’s book, as indicated, e.g., by the paradigmatic importance Whitehead attached to the analogical application of the common math- ematical techniques of trigonometry and harmonic analysis to a wide variety of vibrating and periodic physical systems. “We are here,” Whitehead wrote, “in the presence of one of the fundamental processes of mathematical physics—namely, nothing less than its general method of dealing with the great natural fact of Periodicity.” (IM 143; cf. also SMW 31) However, of the three books mentioned here, the one that influenced Whitehead most was definitely Maxwell’s. Despite some similarity of approach, and even some overlap of con- tent, Maxwell’s Treatise was the most intricate and difficult of the three books, reflecting Maxwell’s immense knowledge of mathematical, theoretical, and experimental electricity and magnetism, as well as his idiosyncratic style of physical reasoning, not adjusted by any prior ex- perience as text book writer, and his liability to overlook errors of varying degrees of seriousness, not corrected for want of a reliable proof reader. Maxwell’s own lectures, unfortunately, were of little help to the first few top students who attempted to work their way through the Treatise. By the time Whitehead wrote his fellowship dissertation on Maxwell’s Treatise, its second edition was available (thanks to W. D. Niven). In this 1882 edition most of the errors were corrected, and some pedagogical clarification was added by means of notes and ap- pendices, and by the fact that some of the most obscure and idiosyncratic passages were rewritten. However, the immensity of the know-how presupposed by and incorporated in the two extensive vol- umes of Maxwell’s book remained an issue. Warwick writes: Maxwell wrote the Treatise for a broad audience, and, to this end, he tried as far as possible to keep advanced mathematical methods, novel physical theory, and electri- 114 Ronny Desmet cal apparatus in respectively separate chapters. […] For Maxwell himself, however, who was fully at home in any area of theoretical and experimental electricity, this divi- sion would have seemed somewhat artificial. He almost certainly hoped that his book would help usher in a new era in university physics in which undergraduates would feel equally at home with higher mathematics, advanced physical theory, and electrical instruments. But in Cam- bridge in the early 1870s there were few if any teachers, apart from Maxwell himself, who possessed the skills re- quired to deal effectively with such a broad range of material. Far from being reunited in undergraduate train- ing, the three strands of electrical studies mentioned above were torn further apart as the Treatise’s contents were fragmented among the three major sites at which physics was taught—the coaching room, the intercollegi- ate classroom, and the Cavendish Laboratory. (288-289) The three distinct strands of electrical science […] implied very different skills on the part of the prospective teacher. The first is the summary of techniques for calculating elec- trostatic and magnetostatic potentials and the electrical current in simple networks of conductors. This aspect of the book was relativity straightforward for mathematical coaches to teach as it required no knowledge of Maxwell’s new field theory, very little knowledge of experimental electricity, and deployed mathematical techniques familiar from other areas of physical science. The second strand is the exposition of Maxwell’s new theory given in the final quarter of the book. This aspect was very difficult for all Cambridge mathematicians to understand and, during the 1870s and early 1880s, was not taught by mathematical coaches but discussed in W. D. Niven’s intercollegiate lec- tures at Trinity College. The third strand concerns the experimental and metrological content of the Treatise. This aspect of the book could neither be taught without practical demonstrations nor actively pursued by students unless they were able to develop skills in the hands-on manipulation of electrical instruments and apparatus. It was on this aspect that Maxwell focused his teaching at the Cavendish Laboratory and in which his first graduate students undertook research. (298) Whitehead’s biographer, Victor Lowe, writes: “I have found no record of Whitehead ever participating in an experiment, and his name is not on any list of those who went to the Cavendish Laboratory.” (97) How- ever, Lowe also referred to Routh as “the man from whom Whitehead got most of his mathematics training” (97), and makes clear that, via  Whitehead’s Cambridge Training 115 his intercollegiate lectures in 1881–1882, “W. D. Niven […] gave Whitehead the most valuable part of his education in mathematical physics.” (94) Consequently, “Routh and Niven gave him the most” (99), and Whitehead’s understanding of Maxwell’s theory was shaped by a combination of Routh’s coaching and Niven’s lecturing. It was an instance of “the collective understanding of electromagnetic field the- ory that emerged in Cambridge circa 1880 [and] was shaped by a combination of the problem-solving approach [of the best Cambridge coaches] and discussions at the intercollegiate lectures on the Treatise held at Trinity College by W. D. Niven.” (Warwick 2003:291) Someone once made the remark to Charles Chree, who became Sixth Wrangler the year Whitehead became Fourth Wrangler, that it would have been an immense improvement to Maxwell’s Treatise to have been written by Routh. And indeed, according to Warwick: As soon as the Treatise appeared, Cambridge’s leading coach, Edward Routh, set to work to master the sections that he thought most relevant to undergraduate studies and to incorporate them in his coaching regime. Routh’s thorough courses already covered most of the important mathematical methods used in the Treatise, and within months of reading the book he had written a new course in which examples from electrostatics, magnetostatics, and current electricity were used as illustrations of these methods. (306) Warwick even holds that “Routh’s teaching of electricity and magnet- ism was almost certainly the most thorough given by any coach in Cambridge” (307), and that he became “a powerful gatekeeper to the mathematical methods necessary to make sense of Maxwell’s book” (315), but he also adds: It is nevertheless a very striking aspect of Routh’s teaching that he introduced these new subjects, at least implicitly, in the form of an action-at-a-distance theory of electricity. This is nicely illustrated by the fact that Routh began his teaching of electromagnetic theory by establishing the in- verse square law of attraction and repulsion for electrostatic force, an exercise calculated to drive home the formal mathematical analogy between gravitational and electrostatic phenomena. Routh in fact made no re- ference at all in his lecture notes to the field-theoretic 116 Ronny Desmet approach adopted by Maxwell in the latter sections of the Treatise, nor did he discuss the electromagnetic theory of light. (307) Routh certainly covered most of the mathematical meth- ods employed in the latter sections, but these were taught in connection with other, more traditional Tripos subjects, such as celestial mechanics and the shape of the earth. The real significance of Routh’s teaching to the study of electromagnetic theory in Cambridge was that it gave able undergraduates a thorough grounding in the principles and application of basic electromagnetic theory and fa- miliarized them with the higher mathematical methods and dynamic concepts they would need if and when they ventured into the final sections of the book. (316-317) The site at which the novel, field-theoretic aspects of Maxwell’s work were first taught and discussed in Cam- bridge was W. D. Niven’s intercollegiate class in electricity and magnetism at Trinity College. (317) At Trinity College, Cambridge, in order to prepare for the most ad- vanced part—Part III—of the Mathematical Tripos examinations of January 1884, and for the Trinity fellowship examinations and disserta- tion of late September, early October 1884, Whitehead attended the intercollegiate course of lectures on electricity and magnetism, which W. D. Niven gave for two terms each year. According to his biographer, Whitehead probably attended Niven’s lectures in 1881–1882, but he adds that it is possible that Whitehead also heard Niven on Maxwell in 1882–1883, because Niven, who was appointed a chair at the Royal Naval College in Greenwich in 1882, probably commuted to Cambridge in 1882-1883 to give his lectures at Trinity for the last time. (Cf. Lowe 1885:95-96) William Davidson Niven was born in Peterhead in 1843, and he died in Sidcup in 1917. Niven was one of three distinguished mathematical brothers. He graduated from the University of Aberdeen in Scotland, not far from Peterhead. From there, as was the tradition of the Scottish Universities at that time, Niven went to study at the University of Cam- bridge. At Cambridge, Niven studied mathematics at Trinity College, where he graduated as Third Wrangler in 1866. The following year he was elected to a Trinity fellowship. Warwick writes: Niven left Cambridge in 1867 to teach mathematical phys- ics in London. Despite his absence from the university,  Whitehead’s Cambridge Training 117 Niven assisted with the introduction of the new physical subjects by acting three times as a Tripos examiner, and in 1874, he was invited to return to his old college as a mathematics lecturer. Whether Niven was appointed spe- cifically to teach the mathematical theory of electricity and magnetism is unclear—he appears to have spent all or part of his first year working on electrical experiments at the Cavendish Laboratory—but he certainly struck up a close friendship with Maxwell and became heir to his sci- entific writings following the latter’s untimely death in 1879. Niven completed the revisions for the second edi- tion of the Treatise and edited the two posthumously published volumes of Maxwell’s collected scientific papers. (318-319) Niven started giving his annual two-term lecture series based on Max- well’s Treatise in 1876, and as said, did so until 1882 or 1883. However, Niven was also one of the three men responsible for the first original contributions to Maxwell’s work in Cambridge. The other two were Charles Niven, one of W. D. Niven’s mathematical brothers, Sen- ior Wrangler in 1867 (beating W. K. Clifford into second place), and Horace Lamb, Second Wrangler in 1872. Warwick refers to these three men as “the first generation of Cambridge Maxwellians.” (325) Niven’s intercollegiate lectures and the research of the first generation of Cambridge Maxwellians cannot be separated. Contrary to Routh, who limited his coaching to an action-at-a-distance approach to elec- tromagnetism, Niven’s lectures and the research of Lamb and the Nivens focused on Maxwell’s novel field-theoretic approach, in which “electromagnetic effects were due almost entirely to the flow of energy in the ether.” (Warwick 2003:329) Like Routh, Lamb and the Nivens displayed “a typical Cambridge understanding of research as a prob- lem-solving exercise,” and “drew heavily upon the methods of physical analogy and mathematical homology.” (Idem 329-330) I already emphasized the importance of the problem-solving methods of physical analogy and mathematical homology when highlighting the influence of Routh on Whitehead’s mature view with regard to the uni- fication of mathematical physics. It is clear that this aspect of Whitehead’s formation can be reemphasized by means of Warwick’s account of Niven’s impact at Cambridge. Moreover, the notion of the 118 Ronny Desmet energy flow in the physical field—the electromagnetic as well as the gravitational field—is a central notion in Whitehead’s writings. In the context of his relativistic theory of gravity, it is closely linked to a no- tion I already mentioned before, the notion of action. But one can also trace the imaginative development of the notion of energy flow in Whitehead’s metaphysical writings (e.g., in PR). Even though Whitehead very often refers to Maxwell’s theory of elec- tricity and magnetism in his writings, he does not mention—not even in his autobiographical notes (cf. ESP 3-14)—Routh’s coaching or Ni- ven’s lecturing, nor his study of, and fellowship dissertation on, Maxwell’s Treatise. Our knowledge of these biographical aspects is indirect. E.g., that the topic of Whitehead’s fellowship dissertation was Maxwell’s Treatise, we know from Betrand Russell’s My Philosophical Development (1959:33). In 1931, in his presidential address to the American Philosophical Association, however, Whitehead made a short reference to his Cambridge training of electricity and magnetism, and more specifically, to the notion of the energy flow in the electromag- netic field. He said: The discussion of the Poynting Flux of Energy is one of the most fascinating chapters of Electrodynamics. Forty-seven years ago, when a young graduate student, I first heard of it in a lecture delivered by Sir J. J. Thomson. It was then a new discovery recently published by Poynting. But its fa- ther was the great Clerk Maxwell who had expounded all the requisite principles. (AI 185) Whitehead referred to J. J. Thomson’s lectures on electromagnetism, which he attended in the term between his Part III Mathematical Tripos exam early 1884, and his Trinity fellowship exam in the fall of that same year. And the quote reveals that it is in these lectures that White- head first heard about J. H. Poynting’s article, written late 1883, published early 1884, and containing Poynting’s famous energy flow theorem, expressing the electromagnetic energy flow as a vector (the Poynting vector) in terms of the (vector product of the) electric and magnetic field-vectors. Routh and Niven are not mentioned in the quote. However, as high- lighted by Andrew Warwick in Masters of Theory, Poynting’s energy  Whitehead’s Cambridge Training 119 flow theorem is one of the most typical products of the nineteenth cen- tury mathematical physics training at Cambridge. In other words, the Poynting theorem case is a paradigmatic case to illustrate the impact of the pedagogical process of training mathematical physics at Cambridge University on the scientific expertise and contributions of its famous graduates. J. H. Poynting—Third Wrangler in 1876—is indeed a prototype. His mixed mathematical expertise was shaped by Routh’s coaching (when Poynting was an undergraduate), Niven’s intercollegiate lectures (after Poynting’s return to Cambridge in 1878), and Poynting’s experimental research under Maxwell at the Cavendish Laboratory. It was also shaped by studying Thomson and Tait’s Treatise of Natural Philosophy, Maxwell’s Treatise on Electricity and Magnetism, and Rayleigh’s Theory of Sound. Poynting arrived at the electromagnetic energy flow theorem in De- cember 1883 by analogy with his November 1883 relation between the energy flow and the velocity of longitudinal and transverse waves in a conducting medium, a relation he found by applying a mathematical technique developed by Rayleigh in his Theory of Sound. Because the November relation was not only applicable to sound waves (longitudi- nal waves), but also to light waves (transverse waves), Poynting set out to interpret it in terms of the electromagnetic theory of light, developed by Maxwell in his Treatise. This way, Poynting found his December expression for the electromagnetic energy flow. Moreover, Warwick also shows how the relevant mathematical technique developed by Rayleigh in his 1877 Theory of Sound is linked to one of the most diffi- cult problems set by Rayleigh as examiner in the 1876 Mathematical Tripos exam, a problem inspired by Rayleigh’s research at that mo- ment in time, and an exam Poynting took that year. Like Poynting, Whitehead could have been taken by Warwick as a prototype of the class of Cambridge men who were trained by both Routh and Niven, and who were moulded by the standard textbooks at the time—a class of which some other members are Joseph Larmor (First Wrangler in 1880), J. J. Thomson (Second Wrangler in 1880) and 120 Ronny Desmet A. R. Forsyth (First Wrangler in 1881). In fact, Larmor, J. J. Thomson, and Poynting, were members of what Warwick calls “the second gen- eration of Cambridge Maxwellians” (333), and Forsyth and Whitehead became both famous Cambridge mathematicians, and good colleagues and friends (cf. Lowe 1985:150-151). Also, like Poynting’s energy flow theorem of electromagnetism, Whitehead’s relativistic theory of gravi- tation could have been taken by Warwick as a typical example of the prominent role of Cambridge’s mixed mathematical training and re- search in the processes that led to its impressive scientific output. In order to substantiate these claims, I now draw together some elements of the above overview, and link them to Whitehead’s philosophy of mathematics, and to his relativistic theory of gravity. 6. Conclusion It is hard to label Whitehead’s philosophy of mathematics. Whitehead himself, in “The Philosophy of Mathematics,” labels the stance he took in his Universal Algebra (UA) as “a formalist position.” (239) Carnap labeled the philosophy of Whitehead and Russell in Principia Math- ematica (PM) as ‘logicism.’ And when we focus on Whitehead’s last philosophical essay, “Mathematics and the Good” (ESP 97-113), and on its thesis that “mathematics is the study of pattern” (106), we are justi- fied to label Whitehead’s philosophy of mathematics as ‘structuralism.’ Of course, one might add that formalism, logicism, and structuralism, after all, have a lot in common, and hence, are not necessarily incom- patible labels. Their respective views that the essence of mathematics consists of the manipulation of symbols, of the deployment of logic, and of the study of patterns, can be harmonized in an overarching view. But even then, none of them perfectly fits Whitehead’s position. To start with, there is the Whiteheadian particularity of talking about mathematics as a mental activity, even one that “enlightens every act of the functioning of the human mind.” (SMW 24) This aspect invites us to conceive of Whitehead as an intuitionist (showing, e.g., with regard to some aspects, a stricking resemblance with Husserl), rather than  Whitehead’s Cambridge Training 121 conceiving him as a stereotype formalist, or as stereotype logicist (if there are such stereotypes to start with). But above all, there is the Whiteheadian particularity of always mixing talk of pure mathematics with talk of applied mathematics. And it is this latter aspect of intimate and fruitful interaction between the realm of the abstract and the realm of the concrete that is clearly linked with his Cambridge training. We cannot understand Whitehead’s search for the universal algebraic formalism, or for the all-pervasive logic of classes and relations, or for the ultimate pattern interweaving all mathematical patterns, without understanding that his ultimate drive was the drive to unify the math- ematical structures underlying the analogical reasonings that constitute the art of physics, an art which his Cambridge training impressed upon him. Only when taking into account the deep impact of this training, we will not be surprised, e.g., that the full title of his Universal Algebra is A Treatise on Universal Algebra, with Applications; that, even prior to publishing the first volume of Principia Mathematica, Whitehead ap- plied its logic of classes and relations to produce a memoir “On Mathematical Concepts of the Material World” (MCMW) and that, while being in the process of writing the (never completed and never pub- lished) fourth volume of Principia Mathematica on geometry, he came up with his own relativistic theories of space-time geometry and gravity. Some more details on the latter theories are revealing. In fact, they bear the clearest marks of Whitehead’s Cambridge training. Thanks to Routh’s coaching and Niven’s intercollegiate lectures, and to the writing of his Trinity fellowship dissertation on Maxwell’s Trea- tise, Whitehead thoroughly studied Faraday’s intuitive, and Maxwell’s mathematical, treatment of the electric and magnetic fields of force. He was highly impressed by Faraday’s speculative vision of a material world resolved into lines of force—especially by Faraday’s 1844 paper in the Philosophical Magazine, “A speculation touching Electric Conduc- tion and the Nature of Matter,” included in Faraday’s 1844 Experimental Researches in Electricity: Volume II (284-293), and (wrongly) referred to by Whitehead (CN 146; instead of 1844, he wrote 1847). “Faraday,” Whitehead wrote, “reorganized the whole theoretical conception of the science [of electricity].” (IM 21) Whitehead was 122 Ronny Desmet equally impressed by Maxwell’s use of analogical reasoning to put Faraday’s ideas “into a directly mathematical form” (Idem)—a topic on which Maxwell himself wrote a paper in 1856, “Are there Real Analo- gies in Nature,” included in Campbell and Garnett’s 1882 The Life of James Clerk Maxwell (235-244). A first example of the impact Faraday and Maxwell made on White- head can be seen in Whitehead’s memoir “On Mathematical Concepts of the Material World.” In “Concept V”—in 1905, this was Whitehead’s preferred logico-mathematical model of space, time, and matter—“the material universe” is resolved into “linear objective reals,” of which Whitehead writes: “they are the lines of force of the modern physicist.” (MCMW 32) This example is relevant here, because the 1905 Concept V can be seen as a spatial precursor of the spatio-temporal theory White- head invented in the 1910s and early 1920s. In that period, Whitehead also assimilated Einstein and Minkowski’s relativity papers. Minkow- ski’s famous 1908 lecture, “Space and Time,” impressed Whitehead the most (even though its influence on Whitehead was postponed ap- proximately ten years). In it, Minkowski expressed his vision of the whole universe as being resolved into electromagnetic world-lines. This sounds familiar. And indeed, Minkowski’s 1908 vision with its universe of world-lines can be conceived as a spatio-temporal equivalent of Faraday’s speculative 1844 vision with its world of spatial lines of force. In fact, Minkowski’s spatio-temporal vision impressed Whitehead so much, and was seen by him as so well in line with the general charac- ter of our sense experience, that he did not accept Einstein’s general relativistic deviation from it in order to solve the problem of formulat- ing a relativistic law of gravity. Hence, Whitehead was faced with the issue to find an alternative, Minkowskian relativistic law of gravity to replace the Einsteinian one. Determined to turn his research into a success story, Whitehead made use of his typical Cambridge problem- solving skills. That is, he tried to solve the problem of finding a relativ- istic theory of gravitational interaction between masses by analogy with Minkowski’s relativistic theory of the electromagnetic interaction be- tween charges. And fortunately for Whitehead, the latter could be formulated in terms of the mathematical techniques of ‘retarded poten-  Whitehead’s Cambridge Training 123 tials,’ and of ‘least action,’ two of the techniques with which each true Cambridge man was familiar, and which could be transferred from the domain of electromagnetism to the domain of gravitation. Moreover, Whitehead had the benefit of being able to also rely on Einstein’s 1916 use of the mathematical technique of ‘coordinate frame independent tensor quantities,’ and on Silberstein’s 1918 critique of Einstein’s solu- tion. And so it happened that he was successful, and that he did in fact find an alternative, Minkowskian relativistic theory of gravity, which, from an empirical point of view, was so close to the Einsteinian theory, that until quite recently, experimenters were unable to discriminate between them. This somewhat simplified account of Whitehead’s path of discovery of a Minkowskian relativistic theory of gravity stenghtens the conclusion of this paper, that a better knowledge of the nature of Whitehead’s Cambridge training does not only lead to a better understanding of the particularity of his philosophy of mathematics, but also of his path of discovery of an alternative relativistic theory of gravity. Cited Works Beets, F. & Dupuis, M. & Weber, M. Editors. (2006) Alfred North Whi- tehead’s Science and the Modern World. Frankfurt: Ontos Verlag, 2006. Campbell, L. & Garnett, W. (1882) The Life of James Clerk Maxwell. London: Macmillan and co., 1882. Campbell, N. R. (1920) Physics, The Elements. Cambridge at the Uni- versity Press, 1920. Duhem, P. (1914) The Aim and Structure of Physical Theory. New York: Atheneum, 1977. Faraday, M. (1844) Experimental Researches in Electricity: Volume II. London: Bernard Quaritch, 1844. 124 Ronny Desmet Hall, R. (2002) “Isaac Newton: Creator of the Cambridge scientific tradition.” (Harman & Mitton 2002:36-50) Harman, P. (1998) The Natural Philosophy of James Clerk Maxwell. Cambridge: Cambridge University Press, 1998. Harman, P. (2002) “Introduction.” (Harman & Mitton 2002:1-5) Harman, P. & Mitton, S. Editors. (2002) Cambridge Scientific Minds. Cambridge: Cambridge University Press, 2002. Hesse, M. (1966) Models and Analogies in Science. Indiana: University of Notre Dame Press, 1970. Hocking, W. E. (1963) “Whitehead as I Knew Him.” (Kline 1963:7-17) Hunt, B. J. (1991) The Maxwellians. Ithica and London: Cornell Uni- versity Press, 1991. Kline, G. L. Editor. (1963) Alfred North Whitehead: Essays on His Phi- losophy. New Jersey: Prentice-Hall, 1963. Lowe, V. (1985) Alfred North Whitehead: The Man and His Work, Vol- ume I: 1861–1910. Baltimore: The John Hopkins University Press, 1985. Minkowski, H. (1908) “Space and Time.” (Sommerfeld 1923:73-96). Nersessian, N. J. (1984) Faraday to Einstein: Constructing Meaning in Scientific Theories. Dordrecht: Kluwer Academic Publishers, 1984. Nersessian, N. J. (2008) Creating Scientific Concepts. Cambridge, MA: The MIT Press, 2008. Richards, J. L. (1988) Mathematical Visions: The Pursuit of Geometry in Victorian England. San Diego, CA: Academic Press, 1988. Riche, J. (2006) “A. N. Whitehead Natural Philosopher.” (Beets & Du- puis & Weber 2006:23-53) Routh, E. J. (1882) The Elementary Part of a Treatise on the Dynamics of a System of Rigid Bodies, Being Part I of a Treatise on the Whole Sub- ject. London: Macmillan, 1882.  Whitehead’s Cambridge Training 125 Russell, B. (1959) My Philosophical Development. London: George Al- len & Unwin, 1975. Silberstein, L. (1918) “General Relativity without the Equivalence Hy- pothesis.” Philosophical Magazine 36: 94-128. Sommerfeld A. Editor. (1923) The Principle of Relativity. New York: Dover, 1952. Temple, G. (1923) “A Generalisation of Professor Whitehead’s Theory of Relativity.” Proceedings of the Physical Society of London 36: 176- 193. Warwick, A. (2003) Masters of Theory: Cambridge and the Rise of Ma- thematical Physics. Chicago and London: The University of Chicago Press, 2003. Wilson, D. B. (1982) “Experimentalists among the Mathematicians: Physics in the Cambridge Natural Sciences Tripos, 1851-1900.” Histori- cal Studies in the Physical Sciences 12: 325-371. Yeo, R. (2002) “William Whewell: A Cambridge historian and philoso- pher.” (Harman & Mitton 2002:51-63) 

spring 2010 Process Perspectives Page 17 Interconnections: News from around the World Applied Process Metaphysics Michel Weber holds an MA and a PhD in philosophy (1991 and 1997). He is the director of the Centre for Philosophical Prac- Summer Institute tice. He has published more than 30 books, e.g., Whitehead’s Pan- creativism: The Basics (2006). T Full program available upon request at info@chromatika. he Centre for Philosophical Practice “Chromatiques white- headiennes” (non-profit org, Brussels, www.chromatika.org) org. Applicants should first contact the organisers to introduce themselves and specify their expectations, and second contact the is organizing its first Applied Process Metaphysics Summer Insti- Foundation to book their accomodation (accueil@fbl-paris.org). tute. It will take place in Paris, at the Cité universitaire’s Fondation The deadline to register for those wishing to stay at the founda- Biermans Lapôtre (www.ciup.fr/fr/les_maisons/fondation_bier- tion is May 31, 2010. Registration fee: 250€ ($330); reduced rate mans_lapotre), on July 27th and 28th. upon request; accomodation fee: 50 € / night ($67). ❧ Applied process metaphysics seeks to provide and to move beyond detailed technical renderings of process philosophy (cf. Dibben and Kelly, Applied Process Thought I, 2008). What mat- ters is personal experience and how to refresh our shared under- New SSPP Listserv standing of experience. T Over the course of two days, participants will have the op- he Society for the Study of Process Philosophies has portunity to travel through most aspects of Whitehead’s legacy: created a new listserv to facilitate communication and the anthropology, ecology, education, epistemology, metaphysics, dissemination of information. To join the list, please visit http:// psychology, political theory, quantum mechanics, and relativity lists.gonzaga.edu/mailman/listinfo/sspp-l . physics. Additionally, some special attention will be devoted to Founded in 1966, SSPP was one of the first satellite organiza- the heuristics of Process and Reality and to the complementarity tions of the American Philosophical Association. The Society is a among its five parts. group of scholars in philosophy and related fields with a specialty Drawing upon the major Harvard works —Science and the or interest in process thought. The Society holds periodic meetings Modern World (1925), Process and Reality (1929), Adventures in conjunction with each of the divisional meetings of the Ameri- of Ideas (1933)—the relevant entries of the Handbook of White- can Philosophical Association, as well as at the annual meeting of headian Process Thought (2008) and on their own most recent the Society for the Advancement of American Philosophy. ❧ research, the instructors will seek, first, to introduce Whitehead’s thought by clarifying what’s at stake in this kind of philosophizing and by providing a synoptic vision of his key categories in light of their historical developments; second, to foster a creative dia- Audio of Lectures Available on logue among all participants; third, to provide assistance on the participants’ own research projects or inquiries. CPS Website To allow this, the work sessions will be paced in the follow- ing way: in the morning, introductory talks on specific epistemic fields; in the afternoon, guided discussions on these fields; at night, private tutorial sessions. We will make sure that Whitehead T he Center for Process Studies maintains a small but growing digital library of multimedia presentations, featuring lectures and seminars from 1972 to the present. is interpreted secundum Whitehead and always bearing actual experience in mind; it makes little sense either to propose an Recently added: exegesis-type of inquiry or to confine it to secondary literature. Papers finalized during the workshops could be submitted to the “Topics in Process Theism,” John B. Cobb, Jr., recorded Octo- Chromatikon Yearbook. ber 22, 2009, at Claremont School of Theology. Instructors are Dr. Ronny Desmet and Dr. Michel Weber. All sessions will be held in English; tutorials could also take place “The Practical Importance of Metaphysics,” John B. Cobb, Jr., in Dutch or in French. An attendance certificate will be provid- recorded February 9, 2010, at Claremont School of Theology. ed on request. A maximum of 15 applications will be accepted. Ronny Desmet holds an MA in mathematics (1983), an MA I’d Rather Be Dead Than Be a Girl, John Sweeney, recorded in philosophy (2005) and a PhD in philosophy (2010). He is cur- March 22, 2010, at Claremont School of Theology. rently research assistant at the Centre of Logic and Philosophy of Science, Free University of Brussels (VUB). His research and Find the collection at http://www.ctr4process.org/media/.❧ publications have focused on Whitehead’s philosophy of math- ematics and relativity.